In order to further test't Hooft's confinement mechanism, we have carried out Monte Carlo calculations of 'abelian' Wilson loops, and the color distribution of electric flux, in certain maximal abelian gauges of SU(2) lattice gauge theory. The electric fl...

Abelian lattice gauge theories coupled to Higgs's fields in the fundamental representation of the gauge group are studied with reference to phase transitions at extreme values of the gauge coupling. The scalar fields are allowed to vary radially and this ...

A new analytical approach based on the use of the dynamical equations in lattice gauge theories (LGT) is presented. The new method is used to discuss the phase structure of abelian lattice gauge systems.

Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in three dimensions. Monopoles are computed by Abelian projection in several gauges, including the maximal Abelian gauge. The number [ital N][sub [ital m

Abelian mechanism of non-Abelian color confinement is observed in a gauge-independent way by high precision lattice Monte Carlo simulations in gluodynamics. An Abelian gauge field is extracted with no gauge fixing. Then we decompose the ...

We explore vortex formation for Abelian projected SU(2) in the Polyakov gauge and compare the results with those calculated in the maximal Abelian gauge. In both gauges, a nonzero vacuum expectation value of a monopole field operator signals confinement. We find vortices in the Polyakov ...

The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields.

The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation ...

The number and the location of the monopoles observed on the lattice in QCD configurations happens to depend strongly on the choice of the gauge used to expose them, in contrast to the physical expectation that monopoles be gauge invariant objects. It is proved by use of the non abelian Bianchi identities (NABI) ...

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational ...

We study the coupling of abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge fields live on dual links. This is the correct formulation if we want to compare the effect of gauge fields on geometry with similar effects studied so far for scalar fields. It shows that ...

A direct connection is proved between the non-Abelian Bianchi Identities (NABI's) and the Abelian Bianchi identities for the 't Hooft tensor. As a consequence, the existence of a nonzero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows us to ...

A direct connection is proved between the non-Abelian Bianchi Identities (NABI�s) and the Abelian Bianchi identities for the �t Hooft tensor. As a consequence, the existence of a nonzero magnetic current is related to the violation of the NABI�s and is a gauge-invariant property. The construction allows us to show that not all ...

We study the dual Higgs theory for the confinement mechanism based on Quantum Chromodynamics (QCD) in the �t Hooft abelian gauge. In the abelian gauge, QCD is reduced into an abelian gauge theory including color-magnetic monopoles, which appear corresponding to the ...

Some recent progresses in three aspects of numerical simulation of non abelian lattice gauge theories coupled to matter fields are reported here: first the simulation of the fermionic part of the Boltzmann factor, second the (quenched) MC analysis of ''bi...

The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimension 2, which in turn should influence the infrared behavior of ghost and gluon ...

The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R ...

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs $n$ internal states of atoms and laser assisted state sensitive tunneling. Thus, dynamics are communicated by unitary $n\\times n$-matrices. By experimental control of the tunneling parameters, the ...

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact Abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the ...

We consider the use of complex stochastic equations in the evaluation of ensemble averages. For a certain class of functions, it is shown how to relate averages over real parameters to those over complex degrees of freedom. We apply these techniques to the Abelian lattice gauge theory and discuss its extension to the ...

We consider abelian chiral gauge theories on the lattice with exact gauge invariance in which the admissible gauge fields are restricted to the ZN subgroup of the original U(1). In the gauge-invariant construction of the original U(1) theory, the gauge ...

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a ...

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a ...

We consider a lattice discretization of a covariantly gauge-fixed Abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we ...

We investigate the properties of the Lieb lattice, that is, a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the ...

We show how the Hamiltonian lattice {ital loop} {ital representation} can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. The lattice loop path integral approach allows us to knit together the power of statistical ...

Quantization techniques for pure non-Abelian gauge fields which avoid the problem of Gribov copies are investigated both in the continuum and on the lattice. The main motivation for such research is that the solution of the Gribov ambiguity is essential in studying nonperturbative aspects of non-Abelian ...

We present numerical evidence that the real-time Hamiltonian dynamics of SU(2) gauge theory on a spatial lattice exhibits deterministic chaos in the semiclassical limit. We determine the largest Lyapunov exponent of the gauge field as a function of energy density, and derive a nonperturbative expression for the thermalization time.

(LGT) [1,2]. In d = 4, this transformation for pure U(1) LGT can be under- stood as the lattice version to non-Abelian LGT in d #21; 2 with a com- pact Lie group G as the gauge group. A simi- lar transformation-Abelian LGT on a d-dimensional hypercubic lattice reads Z = #16;Y i;#22; Z G dg ...

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical ...

We study an extension of the procedure to construct duality transformations among abelian gauge theories to the non abelian case.

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed ...

the structure group of an SU(2) lattice gauge theory (LGT) to a physically equivalent Abelian LGT with a U(1) structure group [6]. The equivariant BRST sym� metry of the partially gauge�fixed LGT was proven to be valid gauge�fixed SU(2)�LGT to the continuum using the equivariant BRST ...

Gauge fixing in the non-perturbative domain of non-Abelian gauge theories is obstructed by the Gribov�Singer ambiguity. To compare results from different methods it is necessary to resolve this ambiguity explicitly. Such a resolution is proposed using conditions on correlation functions for a family of non-perturbative Landau ...

We propose a non-local definition of a gauge-invariant object in terms of the Wilson loop operator in a non-Abelian gauge theory. The trajectory of the object is a closed curve defined by an (untraced) Wilson loop which takes its value in the center of the color group. We show that definition shares basic features with the ...

We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction in the discrete gauge symmetry with respect to the original systems, which corresponds to a generalized mechanism of explicit symmetry ...

The t-expansion is a nonperturbative calculational tool recently developed for Hamiltonian systems. A short review of the method is given. It is followed by a summary of applications to two dimensional spin systems and to four dimensional non-abelian lattice gauge theories. 5 refs., 3 figs.

The publication collects six lectures on the following themes: quantum field theory and classical statistical mechanics, continuous symmetries, lattice gauge theories, the nature of confinement, a criterion for confinement and non-abelian Yang-Mills theor...

OF 3D LGT IN THE PLAQUETTE FORMULATION OLEG BORISENKO, SERGEI VOLOSHIN Institute for Theoretical. Plaquette formulation Lattice gauge theory (LGT) can be formulated in many equivalent ways. The original the dual representation for abelian LGT's was constructed in [2]. Extensions to nonabelian groups have been

Analytic and numerical studies of the lattice gauge theories with both Higgs and fermion fields are reported. A chiral transition is found in a wide class of such theories, both abelian and non-abelian. This transition separates each phase diagram into two regions, one with spontaneous chiral symmetry breaking and ...

The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a ...

In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to ...

A model of confined quarks is presented. It involves an abelian (or nonabelian) gauge field coupled to a quark field. The theory is quantized on a discrete space-time lattice. It shows quark confinement for strong coupling. Specifically, for strong coupling isolated quarks have infinite mass and quark- antiquark pairs with a ...

to reduce the struc� ture group of an SU(2) lattice gauge theory (LGT) to a physically equivalent Abelian LGT with a U(1) structure group 5 . This lattice formulation is the only known definition of an non gauge�fixed SU(2)�LGT to the continuum using the equivariant BRST algebra. Note ...

Gauge Theory (LGT) with an equivariant BRST�symmetry. This Abelian LGT has previ� ously been proven to be physically equivalent to the SU(2)�LGT. Renormalizabil� ity requires a quartic ghost interaction in these non is discussed. 1 Introduction An SU(2) Lattice Gauge Theory (LGT) on a finite ...

After some general remarks on the efficiency of various Monte Carlo algorithms for gauge theories, the calculation of the asymptotic freedom scales of SU(2) and SU(3) gauge theories in the absence of quarks was discussed. There are large numerical factors between these scales when defined in terms of the bare coupling of the lattice ...

It is shown that, after a resummation of leading high-temperature contributions, a complete and gauge-independent result for the non-Abelian Debye screening mass at next-to-leading order can be extracted from the static gluon propagator. In contrast with previous, incomplete results, the correction to the Debye mass is found to be logarithmically sensitive ...

We review the string representations of Abelian-projected SU(2)- and SU(3)-gauge theories and their application to the evaluation of bilocal field strength correlators. The large distance asymptotic behaviours of the latter ones are shown to be in agreement with the Stochastic Vacuum Model of QCD and existing lattice data

We analyze previously proposed order parameters for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory, defined as vacuum expectation value (VEV) of monopole fields in Abelian projection gauges. We show that they exhibit some inconsistency in the treatment of small scales, due to a violation of Dirac ...

Recently, a pair of experiments (Lu et al 2009 Phys. Rev. Lett. 102 030502; Pachos et al 2009 New J. Phys. 11 083010) demonstrated the simulation of Abelian anyons in a spin network of single photons. The experiments were based on the Abelian discrete gauge theory spin lattice model of Kitaev (Kitaev 2003 Ann. ...

. Because of the lattice discretization the algorithm gives rise to speci#12;c lattice artifacts and an e of the Maximal Abelian gauge in this respect. The lattice artifacts are much more di�cult to deal with since a family of spin coherent states j ~n(t) i such that e i'(t) j ~n(t) i = W (t) ...

The formation of monopoles and their condensation in the QCD ground state is a feature which is related to abelian gauge fixing, discussed in this chapter. The gluon field acquires a singularity in the vicinity of points in space where abelian gauge fixing fails and magnetic monopoles are formed there. The ideas ...

The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unifies all classical spin models with apparently very different features in a single ...

The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z{sub 2} LGT. This unifies all classical spin models with apparently very different features in a single ...

The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unifies all classical spin models with apparently very different features in a single ...

We demonstrate the existence of a new topologically ordered phase in Kitaev's honeycomb lattice model. This new phase appears due to the presence of a tightly packed vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its low-energy behavior that is described by four Fermi points as opposed to two Fermi ...

Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of SU(2) lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analyzing their monopole content according to the Polyakov gauge and the maximally ...

The general theme of the workshop concerns techniques for gauge-invariant calculations of off-shell Green's functions in non-Abelian gauge theories such as QCD, and their relationship to other approaches to QCD, including lattice simulations and phenomenology. Of critical interest is the infrared behavior of such ...

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac ...

In 1976 't Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multi-fermion interaction. These old arguments provide a link between a variety of recent and sometimes ...

For non-abelian gauge theories in 3 + 1 dimensions the Monte Carlo studies face considerable obstacles in the limit ( beta = 1/g exp 2 to infinity. It is therefore desirable to complement existing MC studies with studies of a more analytic nature. In this...

Investigations into the nature of possible mechanisms for the confinement of quarks and gluons are reported. Flux patterns in lattice gauge theories are studied with Monte Carlo techniques, and comparisons are made between Abelian and non-abelian theories. The flux patterns associated with the ...

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we study two-dimensional electron gases in a lattice, subjected to such fields. In the continuum limit, the system characterized by a two-component ``magnetic flux" describes a harmonic oscillator existing in two different charge states ...

We review the evidence that the monopoles observed in the lattice simulations of the SU(2) gauge theories exhibit fine-tuning. Which means that at presently available lattices both the non-Abelian action associated with the monopoles and the corresponding entropy factor diverge in the ultraviolet but cancel each ...

We study the weak coupling behaviour of the partition function of non-abelian gauge fields on a finite lattice. Periodic boundary conditions are imposed. Two different power laws in the coupling beta exp -1 arise for the partition function, when the dimen...

Collective oscillations of matter interacting via a classical non-Abelian gauge field are discussed. General equations of motion are derived. Every gauge group is shown to lead to effectively Abelian oscillations corresponding to oscillations of the addit...

We show that the partition function of many classical models with continuous degrees of freedom, e.g. Abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four-dimensional lattice gauge theory (LGT) with ...

It is shown how one can formulate an action principle for classical Abelian gauge theories not by means of gauge potentials and currents but in terms of the gauge invariant field strengths and gauge variant stream potentias. The discussion is on a general...

A confined magnetic flux solution of finite length and finite energy, arising from non-Abelian-gauge theory, is presented. (AIP)

Since Wilson�s work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian ...

We propose an experimental scheme to probe the contribution of a single Dirac cone to the Hall conductivity as a half-odd topological number sequence. In the scheme, the quantum anomalous Hall effect in graphene is simulated with cold atoms trapped in an optical lattice and subjected to a laser-induced non-Abelian gauge field. By ...

We develop an operator formalism for investigating the properties of non-abelian cosmic strings (and vortices) in quantum field theory. Operators are constructed that introduce classical string sources and that create dynamical string loops. The operator construction in lattice gauge theory is explicitly described, and correlation ...

We study the phase structure of the three-dimensional (3D) nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by Monte Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. In contrast to the 3D local ...

We use the duality between the Abelian Higgs model and pure U(1) lattice gauge theory to estimate the ratio ..sqrt..2 kappa equivalent lambda/xi of penetration depth and coherence length at the tricritical point to be ..sqrt..2 kappa roughly-equal 0.93, thus placing the tricritical point slightly on the type-I side of the borderline ...

We investigated topological phases in several decorated lattices such as the square- octagon and spin ruby lattices. The underlying models can be potentially simulated in optical lattices or in multi-orbital transition metal oxides. In the square-octagon lattice we apply a set of non-Abelian ...

We present a new family of gauge invariant non-local order parameters {delta}{sub {alpha}}{sup A} for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite ...

We show how to obtain the dual of any lattice model, with inhomogeneous local interactions, based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains disorder loops on the generators of the cohomology group of a particular dimension. An explicit ...

Generalization of the notion of non-integrable phase is proposed for the case of non-abelian gauge field. It gives an opportunity of the consistent description on non-abelian magnetic charges, if quantization rule is fulfilled. The non-abelian analogies o...

We study the textures of F=2 spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) ...

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of noninteracting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component ...

This paper studies the vacuum overlap order parameter proposed by Fredenhagen and Marcu in the case of the compact U(1) gauge model with the Wilson action coupled to a Higgs field with fixed length |?|=1. The existence of two distinct phases in D space-time dimensions ( D?4) is established.

The interaction between magnetic monopoles and electric flux tubes is shown to be repulsive to all orders in strong-coupling perturbation theory for a U(1) lattice gauge theory. The significance of this result and the possibility of extension to non-Abelian theories is discussed. For SU(3), the interaction energy is computed to lowest ...

Confinement in non-Abelian gauge theories is commonly ascribed to percolation of magnetic monopoles, or strings in the vacuum. At the deconfinement phase transition the condensed magnetic degrees of freedom are released into gluon plasma as thermal magnetic monopoles. We point out that within the percolation picture, lattice ...

We analyze the interplay of topological objects in four dimensional QCD. The distributions of color magnetic monopoles obtained in the maximum abelian gauge are computed around instantons in four-dimensional full QCD. We find an enhanced probability of encountering monopoles inside the core of an instanton. Moreover we present evidence that nontrivial ...

An example of a local lattice hamiltonian in three space dimensions whose continuum limit spectrum consists of a single free Weyl particle and a set of non-propagating modes is presented. Our model satisfies all the hypotheses of the Nielsen-Ninomiya theorem. However, when locally coupled to a background abelian gauge field, it fails ...

Abelian Monopole and Center Vortex Views at the Multi�Instanton Gas M. Fukushima y z , E.--M. Ilgenfritz x of the vacuum. Over the last years the results have not much converged (compare the recent conference reports�graining of a continuum model. In a lattice gauge theory investigation the role of the discretization scale a would

In this paper gauge theories are analyzed from the point of view of constructive quantum field theory. Diamagnetic inequalities for general lattice gauge theories are proven. They say that in a local field theory the ground-state energy density rises when the fields (scalars, Dirac fields, etc.) are minimally coupled to an external ...

We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical ...

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory in 5 dimensions for small R. (2) It is equivalent to the Lorentz-invariant theory of ...

This thesis describes the coherent state variational algorithm, its implementation in a recently completed set of computer programs, and its application to the study of the QCD deconfinement phase transition. The coherent state variational algorithm is a computational method for studying the large-N limit of non-abelian gauge theories by direct ...

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions to sets of Abelian plane wave configurations of varying amplitude and wavelength, and sets of ...

The set-up of the QCD Schr�dinger functional (SF) on the lattice with staggered quarks requires an even number of points L/ a in the spatial directions, while the Euclidean time extent of the lattice, T/ a, must be odd. Identifying a unique renormalisation scale, L = T, is then only possible up to O( a) lattice artefacts. In this ...

The connection between the Fermi-Walker transport and the Weyl non-Abelian gauge field is established. A theoretical possibility of detecting the Weyl gauge field caused by the Thomas precession of a gyroscope is discussed 7 refs. Submitted to Internation...

It is shown that the congruent transference introduced by Weyl in 1921 defines a non-Abelian gauge field. The simplest gauge-invariant equations are proposed for this field. Connection with the Riemann-Cartan geometry is discussed. 6 refs. (Atomindex cita...

On the basis of global Abelian gauge invariant classical field theoretical models, the problem of existence of hidden symmetry with respect to some nonlocal gauge transformations without including compensating fields is investigated. In the 2-dimensional ...

review briefly how and why our attention was drawn to the non�Abelian gauge theory in describing strong to the dielectric constant of the vacuum in QED is the inverse of the renormalization constant of the color gauge is a consequence of an unbroken non�Abelian gauge symmetry and the ...

The simplest form of the Langevin equation for axial-gauge non-Abelian gauge theory fails to reproduce correctly a Wilson-loop calculation.

The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory ...

A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z{sub 2} gauge field. A phase diagram in the parameter space is ...

Which gauge transformations are symmetries (in the sense of Schwarz, and Forgacs and Manton) of a given gauge field configuration. First, in topologically non-trivial gauge theories there may be an obstruction for implementing gauge transformations on the...

A model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SUq(2), qn=1, it is the Turaev-Viro invariant and the model may be regarded as a nonperturbative definition of 3D simplicial quantum gravity. If one takes a ...

We demonstrate the existence of a topologically ordered phase in Kitaev�s honeycomb lattice model. This phase appears due to the presence of a vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its low-energy behavior that is described by a distinct number of Dirac fermions. We identify two physically ...

We analyze the Hamiltonian time evolution of classical SU(2) Yang-Mills-Higgs theory with a fundamental Higgs doublet on a spacial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Lyapunov exponents under randomized initial conditions in the weak-coupling regime, where one ...

In this paper, a model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SU{sub q}(2), q{sup n} = 1, it is the Turaev-Viro invariant and the model may be regarded as a non-perturbative definition of 3D simplicial ...

For both Abelian and non-Abelian gauge theories, we find gauge transformations which map fields in the U gauge to other fields in the U gauge. These transformations are not contained in the surviving gauge symmetry after spontaneous breaking (defined as ...

We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in bbfR(sup 3) can be defined so that its large-mass limit be the renormalized vaccum expectation value of the Wilson loop for abelian...

We present solutions of coupled particle-field evolution in classical U(1) and SU(2) gauge theories in real time on three-dimensional lattices. Our simulations are performed in a regime of extreme anisotropy of the momentum distribution of hard particles where backreaction is important. We find qualitatively different behavior for the two theories when the ...

We show that loop wave equations in non-Abelian Chern-Simons gauge theory are exactly solved by a conformally invariant topological fermionic string theory.

Within the context of an Abelian Gauge Theory, phase transition driven by the spontaneous generation of domain walls is discused. The critical temperature is calculated semiclassically. The results are very close to those obtained via the effective potent...

We (try to) pedagogically explain how monopoles arise in QCD, why maximal Abelian (MA) gauge is ''special'' for monopole study, the Abelian projection in MA gauge, its resultant degrees of freedom (photons, monopoles and charged matter fields), and the QC...

A massive Abelian gauge field coupled with a non-conserved mass-changing current is described within the framework of canonical quantum theory with indefinite metric. In addition to the conventional Lagrange multiplier field, another ghost field is introd...

A simple and systematic method for the calculation of group-theoretic weights associated with Feynman diagrams in non-Abelian gauge theories is presented. Both classical and exceptional groups are discussed. (AIP)

The dynamic mechanism of spontaneous breakdown of chiral invariance in non-abelian gauge theories is proposed. The spectrum of the quark dynamical masses in quantum chromodynamics is found. (Atomindex citation 12:582720)

I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.

I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.

I review current theoretical evidence for the coexistence of asymptotic freedom and quark confinement in a non-Abelian gauge theory of the strong interaction.

... (Author). Descriptors : *COMMUTATORS, *ELECTROMAGNETIC FIELDS, *GROUPS(MATHEMATICS), ALGEBRAIC TOPOLOGY, DIFFERENTIAL ...

Hamiltonian lattice perturbation methods are used to study the (1 + 1) -dimensional, SU(2) -flavor Abelian gauge model. For a model with coupling constant g and fermion mass m, two distinct vacuum regions characterized by the magnitude of m/g are found. Expansions about the Ising-type vacuum corresponding to large m/g are carried out ...

This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was ...

The basic set of gauge-invariant local as well as nonlocal fields is constructed for a non-Abelian pure gauge theory with the gauge group SU({ital N}). It is shown that the basic set of local gauge-invariant fields are local generators of the nonlocal gauge-invariant ...

It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry. (auth)

The Abelian charges in a non-Abelian Yang-Mills-Dirac theory arising from the reduction of the structure group are studied. They are defined by the concept of the stabilizer gauge transformations. Their properties are investigated. The relationship between the whole class of stabilizer and the stratification of the space of ...

We give a prescription which determines the otherwise ambiguous operator for time-independent non-Abelian gauge transformation with change of topological charge.

Generalizing an earlier work on the Abelian case the most general non-Abelian gauge theory in two spatial dimensions is derived. It is shown that local gauge invariance leads to a new term in the action which in turn requires that the gauge current operator have a part which is bilinear in the ...

We discuss the quantization of chiral gauge theories by lattice regularization, carefully treating the effects of the chiral anomaly. We derive a chiral gauge invariant lattice fermion action from a chiral gauge variant Wilson fermion action without chang...

seemed not to be fundamental . I explain in more detail below. #12;GAUGE THEORY (Non Abelian) Classically-abelian guage theories can (depending on details) behave very different from their classical counterparts Let usTHE GRAVITY-GAUGE THEORYTHE GRAVITY-GAUGE THEORY CORRESPONDENCECORRESPONDENCE ...

In this paper by using the BRST invariance, the authors discuss the stochastic gauge-fixing function which corresponds to the ordinary gauge-fixing function for non-Abelian antisymmetric tensor fields as reducible gauge theories. Then the trail stochastic gauge-fixing function is obtained ...

All order Seiberg-Witten maps of gauge parameter, gauge field, and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order ...

Recently an interesting idea has been put forward by Robinson and Wilczek that the incorporation of quantized gravity in the framework of Abelian and non-Abelian gauge theories results in a correction to the running of gauge coupling and, as a consequence, increase the grand unification scale and asymptotic ...

Gauge conditions in non-Abelian gauge theories are considered studying unitarity with a given Lagrangian with various linear gauge conditions and using the usual formalism for constructing the fictitious Lagrangian. The results show that even with the fulfillment of certain requirements the theory may have ...

We extend the Olesen approach to confinement, originally proposed for SU(?) gauge theory, to the SU(2) group. We perform Monte Carlo calculations of the spectral density, which describes the distribution of eigenvalues of the Wilson loop in the SU(2) lattice gauge theory (LGT), for square loops up to size 4 � 4. Our results indicate ...

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.

Recent research on lattice gauge theories is reviewed, with particular emphasis being placed on numerical results from Monte Carlo simulations.

V A Fock, in 1926, was the first to have the idea of an Abelian gradient transformation and to discover that the electromagnetic interaction of charged particles has a gradient invariance in the framework of quantum mechanics. These transformation and invariance were respectively named Eichtransformation and Eichinvarianz by H Weyl in 1929 (the German verb zu eichen means to ...

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity, ...

The authors study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. A comparison is presented of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models ...

A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this ...

We study the subdivision properties of certain lattice gauge theories based on the discrete Abelian group Zp, in four dimensions. The Boltzmann weights are shown to be invariant under all type (k, l) subdivision moves, at certain discrete values of the coupling parameter. The partition function then provides a combinatorial invariant ...

We discuss the covariant formulation of the dynamics of particles with Abelian and non-Abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply ...

Assuming that a lattice gauge theory describes a fundamental attribute of Nature, it should be pointed out that such a theory in the form of a gauge glass is a weaker assumption than a regular lattice model in as much as it is not constrained by the impos...

This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Using renormalization group equations for the SM, ...

We show that the introduction of massless fermions in an abelian gauge theory in 2+1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarization tensor. However, parity anomaly does exist in non-abelian theories due to a conflict between ...

Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ''vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. ...

It is shown that the hypothesis that bound states are generated by weak interactions between leptons might be at the origin of Yang--Mills gauge fields; and it is shown how the Abelian or nonAbelian gauge transformations of the gauge fields might be due to that of the constituent spinor ...

The formalism of Pugh's asymptotic field theory is applied here to the problem of quantizing non-Abelian gauge fields. The advantage of this formalism is that no ultraviolet divergences ever appear when one performs perturbation theory calculations for S-matrix elements. By fixing the form of the gauge transformation for the ...

The dual transformation discovered in the two-dimensional Ising and planar Heisenberg models is applied to gauge theories in four dimensions. It is shown that after the dual transformation the Abelian Higgs model gives the same partition function as the relativistic hydrodynamics of Kalb and Ramond and of Nambu coupled to the Higgs scalar, and that these ...

We propose a scheme to realize Zitterbewegung (ZB) with cold atoms in an Abelian vector potential. Two dark states can be created by interacting alkali-metal atoms with three coaxial Gaussian beams. Atoms moving in the subspace spanned by the two dark states feel a vector gauge potential that is nonvanishing only along the laser axis. We show that cold ...

We propose an efficient variational method for Z(sup 2) lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when on...

A general, regularization-scheme-independent proof of the nonrenormalization theorem for the anomaly of a U(1) axial current in a renormalizable gauge theory is presented. The gauge group may be an arbitrary compact Lie group. The validity of the theorem is traced back to some finiteness properties allowing for a well defined but particular choice of the ...

Using the simplicial pseudorandom version of lattice gauge theory, we study simple Z(n)-gauge models in D = 3 dimensions. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudorandom lattice. Calcu...

We show that chiral gauge theoreis can be put on a lattice by exploiting the idea of adding extra degrees of freedom. We also examine the lattice chiral Schwinger model to find that the gauge interaction imposes a restriction on the values of a parameter peculiar to the lattice fermion.

As a first step towards a duality transformation for the SU(2) lattice gauge theory in 3 dimensions, the integration over all gauge variant variables is performed explicitly after introducing gauge invariant auxiliary variables. The resulting new Hamilton...

After some general remarks on the efficiency of various Monte Carlo algorithms for gauge theories, the calculation of the asymptotic freedom scales of SU(2) and SU(3) gauge theories in the absence of quarks was discussed. There are large numerical factors...

The gauge dependence of the effective action of quantum non-Abelian gauge theories is studied. An alternative effective action is proposed and its equivalence with the usual effective action is discussed, as well as the equivalence with 't Hooft's effective action.

We consider the possibility that the gauge theory of quarks and gluons is realized as that of baryons and vector baryoniums. The discussion relies on the following two assumptions: (1) the confined and Higgs phases of certain non-Abelian gauge theories ar...

Dirac's theory of magnetic monopoles is extended to the case of non- Abelian color gauge groups. The exact classical solution is obtained by making use of the gauge-independent method of a Yang-Mills field. The case of broken gauge symmetry is also briefly discussed. (NL)

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' ...

We probe for operators occurring in the APQCD (Abelian-projected QCD) action by evaluating Abelian-projected one-plaquette spectral densities in pure gauge SU(3) fixed to the maximal Abelian gauge. Couplings {ital {bar B}}{sub APQCD}({ital q},{ital L}) are extracted from the spectral densities ...

The physical content of nonrelativistic quantum field theory with non-Abelian Chern-Simons interactions is clarified with the help of the equivalent first-quantized description which we derive in any physical gauge.

We show that the non-Abelian magnetic monopole defined in a gauge-invariant way in SU(3) Yang-Mills theory gives a dominant contribution to confinement of the fundamental quark, in sharp contrast to the SU(2) case.

The BRST invariance of theories with local space-time symmetries, such as the reparametrization-invariant point-particle or d-dimensional general relativity, and of theories with local internal symmetries, like abelian and non-abelian gauge theories, can ...

The abelian generalization of QED sub 2 to include SU(M) flavor and diagonal SU(N) color is considered. The operator solutions and confinement aspects of these models are discussed in detail for the case of massless and massive fermions. For a non-vanishi...

Presented is a detailed study of chiral-symmetry breaking in the semiclassical approximation of the two-dimensional Abelian Higgs model with massless fermions. Emphasis is on examining the consistency of the dynamical symmetry-breaking mechanism with the requirements of gauge invariance.

A formal proof and explicit check of unitarity for non-Abelian gauge theories with a particular bilinear gauge condition are presented. The theories are constructed within the Lagrange-multiplier formalism. It is concluded that the usual formalism for non-Abelian gauge theories is not ...

We present Monte Carlo simulations on a new class of lattice models in which the degrees of freedom are elements of an abelian or non-abelian finite group G, placed on directed edges of a two-dimensional lattice. The group product around any plaquette is constrained to be the group identity, as in a discrete ...

The fundamental theory of the geometric phase is summarized in a way suitable for use in molecular systems treated by the Born-Oppenheimer approach. Both Abelian and non-Abelian cases are considered. Applications discussd include the Abelian geometric phase associated with an intersection of two electronic potential-energy surfaces; ...

We construct a classical action for a system of N point-like sources which carry SU(2) non-Abelian charges coupled to non-Abelian Chern-Simons gauge fields, and we develop a quantum mechanics for them. Adopting the coherent state quantization and solving the Gauss` constraint in an appropriately chosen gauge, we ...

We consider the bosonic fractional quantum Hall (FQH) effect in the presence of a non-Abelian gauge field in addition to the usual Abelian magnetic field. The non-Abelian field breaks the twofold internal state degeneracy, but preserves the Landau level degeneracy. Using exact diagonalization, we find that for ...

After briefly reviewing the problems associated with non-Abelian monopoles, we turn our attention to the development in our understanding of non-Abelian vortices in the last several years. In the U(N) model with Nf = N flavors in which they were first found, the fluctuations of the orientational modes along the vortex length and in time become strongly ...

We re-examine the work of Antoniadis et al.[1] on the apparent gauge-parameter dependence of the mass counterterm for a scalar field coupled to gravity and show that the same effect appears in a spontaneously broken abelian Higgs model. In both cases the Nielsen identities assure the gauge-parameter independence of the pole masses. ...

We consider the finite-action classical solutions of Euclidean topologically massive gauge theories in the presence of external sources. We study the Abelian case for general sources, as well as the general non-Abelian case for weak sources. We also investigate the solutions within the radial {ital Ansatz}, both with the usual source ...

An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstr�m-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstroem-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a ...

An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner Nordstr�m anti de Sitter solutions from a family of symmetry-breaking solutions which preserve a ...

We give an argument for deriving analytically the infrared Abelian dominance in a gauge-invariant way for the Wilson loop average in SU(2) Yang-Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color ...

Lattice theory in mechanics and quantum mechanics is introduced. Ways of solving the harmonic oscillator problem; fields; thermodynamics and statistical mechanics; latticization; gauge fields on a lattice; and quantum chromodynamic observables are discuss...

In equilibrium, at finite temperature below and above the deconfining phase transition, we have generated lattice SU(2) gauge fields and have exposed them to smearing in order to investigate the emerging clusters of topological charge. Analyzing in addition the monopole clusters according to the maximally Abelian ...

The gravitational corrections to the gauge coupling constants of Abelian and non-Abelian gauge theories have been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors from different approaches. We propose to discuss this issue from a ...

The method of Parisi and Wu of quantizing gauge theories (stochastic quantization) is reformulated using path integrals. We first review how the gauge fixing enters through the initial condition of the associated Langevin equation. We then prove, nonperturbatively, how the contribution of the Faddeev-Popov determinant is naturally generated by the ...

An abelian gauge theory with violation of P and T symmetries, is constructed other features of usual spinor quantum electrodynamics are maintained. The theory is applied to some scattering processes with polarized and unpolarized electrons. (Atomindex cit...

When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a BANDF coupling and a kinetic term for B is included, the gauge field develops an effective mass. The theory can be made invariant under a non-Abelian vector gauge symmetry by introducing an auxiliary vector field. The ...

We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising ...

We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative ...

We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative problem.

The hard-thermal-loop perturbation theory (HTLpt) framework is used to calculate the thermodynamic functions of a quark-gluon plasma to three-loop order. This is the highest order accessible by finite temperature perturbation theory applied to a non-Abelian gauge theory before the high-temperature infrared catastrophe. All ultraviolet divergences are ...

We investigate the chiral properties of QCD in the presence of a magnetic background field and in the low temperature regime, by lattice numerical simulations of Nf=2 QCD. We adopt a standard staggered discretization, with a pion mass around 200 MeV, and explore a range of magnetic fields (180MeV)2?|e|B?(700MeV)2, in which we study magnetic catalysis, i.e. the increase of ...

We solve the coupled Wong Yang Mills equations for both U(1) and SU(2) gauge groups and anisotropic particle momentum distributions numerically on a lattice. For weak fields with initial energy density much smaller than that of the particles we confirm the existence of plasma instabilities and of exponential growth of the fields which has been discussed ...

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms ...

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms ...

We examine current-carrying configurations of cosmic strings in non-Abelian gauge theories. We study the solutions numerically and point out that the currents will be at best {ital dynamically} stable and not subject to any topological quantization or conservation, as in conventional models of string superconduction. We suggest that ...

We examine current-carrying configurations of cosmic strings in non-Abelian gauge theories. We study the solutions numerically and point out that the currents will be at best dynamically stable and not subject to any topological quantization or conservation, as in conventional models of string superconduction. We suggest that ...

Based on the strong magnetic anisotropy along the symmetry of the crystal, we construct a U(2) non-Abelian gauge potential for the molecular nanomagnet Mn12 by varying the external magnetic field adiabatically. Moreover, the non-Abelian geometric phase and the unitary matrix operation, which are the key steps to realize the universal ...

We prove the Stokes theorem for non-Abelian gauge fields using general surface coordinates. Our result contains both of the known versions of the non-Abelian Stokes theorem and allows us to get a new one which is explicitly invariant under rotations of coordinates.

We study the application of the ''leapfrog'' method of finite differencing to the approximate solution of operator equations of motion in quantum theory. We show that, for a wide class of linear and nonlinear systems, the leapfrog differencing scheme is exactly unitary. The method is sufficiently general to apply to many-particle systems with arbitrary potential ...

in Lattice Gauge Theory A longstanding problem in Lattice Gauge Theory (LGT) is that of a first principles determination of the Gluon Condensate (GC). In LGT the GC is given in terms of Wilson Loops, for instance

We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon ...

The conditions of local gauge invariance under a general non-Abelian group are discussed. They imply the field equations for the gauge vector fields and the existence of conserved Noether's currents of global gauge invariance. There are no extra conserved currents associated with local ...

A discussion is presented on the renormalization of Wilson operators, which are relevant for the radiative corrections to hadrons, in covariant Lorentz gauges, for a class of non-Abelian gauge theories. For the anomalous dimensions of the operators, which determine the asymptotic behavior of the radiative corrections, the same ...

The Dyson-Schwinger equations (DSEs) are a tower of coupled integral equations that relate the Green functions of QCD to one another. Solving these equations provides the solution of QCD. This tower of equations includes the equation for the quark self-energy, which is the analogue of the gap equation in superconductivity, and the Bethe-Salpeter equation, the solution of which is the ...