Gauge Gravity and Electroweak Theory

NASA Astrophysics Data System (ADS)

Hestenes, David

2008-09-01

Reformulation of the Dirac equation in terms of the real Spacetime Algebra (STA) reveals hidden geometric structure, including a geometric role for the unit imaginary as generator of rotations in a spacelike plane. The STA and the real Dirac equation play essential roles in a new Gauge Theory Gravity (GTG) version of General Relativity (GR). Besides clarifying the conceptual foundations of GR and facilitating complex computations, GTG opens up new possibilities for a unified gauge theory of gravity and quantum mechanics, including spacetime geometry of electroweak interactions. The Weinberg-Salam model fits perfectly into this geometric framework, and a promising variant that replaces chiral states with Majorana states is formulated to incorporate zitterbewegung in electron states.

Digital quantum simulation of Dirac equation with a trapped ion

NASA Astrophysics Data System (ADS)

Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration

2014-05-01

Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.

Dual Vector Spaces and Physical Singularities

NASA Astrophysics Data System (ADS)

Rowlands, Peter

Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

Simple and accurate sum rules for highly relativistic systems

NASA Astrophysics Data System (ADS)

Cohen, Scott M.

2005-03-01

In this paper, I consider the Bethe and Thomas-Reiche-Kuhn sum rules, which together form the foundation of Bethe's theory of energy loss from fast charged particles to matter. For nonrelativistic target systems, the use of closure leads directly to simple expressions for these quantities. In the case of relativistic systems, on the other hand, the calculation of sum rules is fraught with difficulties. Various perturbative approaches have been used over the years to obtain relativistic corrections, but these methods fail badly when the system in question is very strongly bound. Here, I present an approach that leads to relatively simple expressions yielding accurate sums, even for highly relativistic many-electron systems. I also offer an explanation for the difference between relativistic and nonrelativistic sum rules in terms of the Zitterbewegung of the electrons.

Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

2018-04-01

We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

Position, spin, and orbital angular momentum of a relativistic electron

NASA Astrophysics Data System (ADS)

Bliokh, Konstantin Y.; Dennis, Mark R.; Nori, Franco

2017-08-01

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We consider two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the Zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K. Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011), 10.1103/PhysRevLett.107.174802] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S. M. Barnett, Phys. Rev. Lett. 118, 114802 (2017), 10.1103/PhysRevLett.118.114802].

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cirilo-Lombardo, Diego Julio; Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna

The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoreticalmore » procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.« less

Gouy phase for relativistic quantum particles

NASA Astrophysics Data System (ADS)

Ducharme, R.; da Paz, I. G.

2015-08-01

Exact Hermite-Gaussian solutions to the Klein-Gordon equation for particle beams are obtained here that depend on the 4-position of the beam waist. These are Bateman-Hillion solutions that are shown to include Gouy phase and preserve their forms under Lorentz transformations. As the wave function contains two time coordinates, the particle current must be interpreted in a constraint space to reduce the number of independent coordinates. The form of the constraint space is not certain except in the nonrelativistic limit, but a trial form is proposed, enabling the observable properties of the beam to be calculated for future comparison to experiment. These results can be relevant in the theoretical development of singular electron optics since it was shown that the Gouy phase is crucial in this field as well as to investigate a possible Gouy phase effect in Zitterbewegung phenomenon of spin-zero particles. Additionally, the traditional argument that beam solutions belong to a complex shifted spacetime is shown to necessitate a corresponding Born reciprocal shift in 4-momentum space.

Surface phononic graphene

NASA Astrophysics Data System (ADS)

Yu, Si-Yuan; Sun, Xiao-Chen; Ni, Xu; Wang, Qing; Yan, Xue-Jun; He, Cheng; Liu, Xiao-Ping; Feng, Liang; Lu, Ming-Hui; Chen, Yan-Feng

2016-12-01

Strategic manipulation of wave and particle transport in various media is the key driving force for modern information processing and communication. In a strongly scattering medium, waves and particles exhibit versatile transport characteristics such as localization, tunnelling with exponential decay, ballistic, and diffusion behaviours due to dynamical multiple scattering from strong scatters or impurities. Recent investigations of graphene have offered a unique approach, from a quantum point of view, to design the dispersion of electrons on demand, enabling relativistic massless Dirac quasiparticles, and thus inducing low-loss transport either ballistically or diffusively. Here, we report an experimental demonstration of an artificial phononic graphene tailored for surface phonons on a LiNbO3 integrated platform. The system exhibits Dirac quasiparticle-like transport, that is, pseudo-diffusion at the Dirac point, which gives rise to a thickness-independent temporal beating for transmitted pulses, an analogue of Zitterbewegung effects. The demonstrated fully integrated artificial phononic graphene platform here constitutes a step towards on-chip quantum simulators of graphene and unique monolithic electro-acoustic integrated circuits.

Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

NASA Astrophysics Data System (ADS)

Tsai, Hung-Ming; Poirier, Bill

2016-03-01

In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

Does Bohm's Quantum Force Have a Classical Origin?

NASA Astrophysics Data System (ADS)

Lush, David C.

2016-08-01

In the de Broglie-Bohm formulation of quantum mechanics, the electron is stationary in the ground state of hydrogenic atoms, because the quantum force exactly cancels the Coulomb attraction of the electron to the nucleus. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the Zitterbewegung interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.

Dirac Cellular Automaton from Split-step Quantum Walk

PubMed Central

Mallick, Arindam; Chandrashekar, C. M.

2016-01-01

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory. PMID:27184159

Hunting for Snarks in Quantum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hestenes, David

2009-12-08

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it ismore » an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.« less

Wavefunction Collapse via a Nonlocal Relativistic Variational Principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, Alan K.

2012-06-18

Since the origin of quantum theory in the 1920's, some of its practitioners (and founders) have been troubled by some of its features, including indeterminacy, nonlocality and entanglement. The 'collapse' process described in the Copenhagen Interpretation is suspect for several reasons, and the act of 'measurement,' which is supposed to delimit its regime of validity, has never been unambiguously defined. In recent decades, nonlocality and entanglement have been studied energetically, both theoretically and experimentally, and the theory has been reinterpreted in imaginative ways, but many mysteries remain. We propose that it is necessary to replace the theory by one thatmore » is explicitly nonlinear and nonlocal, and does not distinguish between measurement and non-measurement regimes. We have constructed such a theory, for which the phase of the wavefunction plays the role of a hidden variable via the process of zitterbewegung. To capture this effect, the theory must be relativistic, even when describing nonrelativistic phenomena. It is formulated as a variational principle, in which Nature attempts to minimize the sum of two spacetime integrals. The first integral tends to drive the solution toward a solution of the standard quantum mechanical wave equation, and also enforces the Born rule of outcome probabilities. The second integral drives the collapse process. We demonstrate that the new theory correctly predicts the possible outcomes of the electron two-slit experiment, including the infamous 'delayed-choice' variant. We observe that it appears to resolve some long-standing mysteries, but introduces new ones, including possible retrocausality (a cause later than its effect). It is not clear whether the new theory is deterministic.« less

Semirelativity in semiconductors: a review.

PubMed

Zawadzki, Wlodek

2017-09-20

in crossed electric and magnetic fields are described theoretically and experimentally. It is only the two-band description for NGS, equivalent to the Dirac or Klein-Gordon equations for free particles, that gives a correct account of experimental results in this situation. A transverse Doppler shift in the cyclotron resonance observed in crossed fields in InSb indicates that there exists a time dilatation between an oscillating electron and an observer. The phenomenon of Zitterbewegung (ZB, trembling motion) for electrons in NGS is considered theoretically, following the original proposition of Schrödinger for free relativistic electrons in vacuum. The two descriptions are in close analogy, but the frequency of ZB for electrons in NGS is orders of magnitude lower and its amplitude orders of magnitude higher making possible experimental observations in semiconductors considerably more favorable. Finally, graphene and carbon nanotubes, as well as topological insulators are considered in the framework of relativistic analogy. These systems, with their linear energy-quasimomentum dispersions, illustrate the extreme semirelativistic regime. Experimental results for the energy dispersions and the Landau quantizations in the presence of a magnetic field are quoted and their analogy to the behavior of free relativistic electrons is discussed. Approximations and restrictions of the relativistic analogy are emphasized. On the other hand, it is indicated that in various situations it is considerably easier to observe semirelativistic effects in semiconductors than the relativistic effects in vacuum.

Semirelativity in semiconductors: a review

NASA Astrophysics Data System (ADS)

Zawadzki, Wlodek

2017-09-01

energy. This conclusion is confirmed experimentally for NGS. Electrons in crossed electric and magnetic fields are described theoretically and experimentally. It is only the two-band description for NGS, equivalent to the Dirac or Klein-Gordon equations for free particles, that gives a correct account of experimental results in this situation. A transverse Doppler shift in the cyclotron resonance observed in crossed fields in InSb indicates that there exists a time dilatation between an oscillating electron and an observer. The phenomenon of Zitterbewegung (ZB, trembling motion) for electrons in NGS is considered theoretically, following the original proposition of Schrödinger for free relativistic electrons in vacuum. The two descriptions are in close analogy, but the frequency of ZB for electrons in NGS is orders of magnitude lower and its amplitude orders of magnitude higher making possible experimental observations in semiconductors considerably more favorable. Finally, graphene and carbon nanotubes, as well as topological insulators are considered in the framework of relativistic analogy. These systems, with their linear energy-quasimomentum dispersions, illustrate the extreme semirelativistic regime. Experimental results for the energy dispersions and the Landau quantizations in the presence of a magnetic field are quoted and their analogy to the behavior of free relativistic electrons is discussed. Approximations and restrictions of the relativistic analogy are emphasized. On the other hand, it is indicated that in various situations it is considerably easier to observe semirelativistic effects in semiconductors than the relativistic effects in vacuum.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ling, Meng-Chieh

Graphene, a two-dimensional (2D) honeycomb structure allotrope of carbon atoms, has a long history since the invention of the pencil [Petroski (1989)] and the linear dispersion band structure proposed by Wallace [Wal]; however, only after Novoselov et al. successively isolated graphene from graphite [Novoselov et al. (2004)], it has been studied intensively during the recent years. It draws so much attentions not only because of its potential application in future electronic devices but also because of its fundamental properties: its quasiparticles are governed by the two-dimensional Dirac equation, and exhibit a variety of phenomena such as the anomalous integer quantummore » Hall effect (IQHE) [Novoselov et al. (2005)] measured experimentally, a minimal conductivity at vanishing carrier concentration [Neto et al. (2009)], Kondo effect with magnetic element doping [Hentschel and Guinea (2007)], Klein tunneling in p-n junctions [Cheianov and Fal’ko (2006), Beenakker (2008)], Zitterbewegung [Katsnelson (2006)], and Schwinger pair production [Schwinger (1951); Dora and Moessner (2010)]. Although both electron-phonon coupling and photoconductivity in graphene also draws great attention [Yan et al. (2007); Satou et al. (2008); Hwang and Sarma (2008); Vasko and Ryzhii (2008); Mishchenko (2009)], the nonequilibrium behavior based on the combination of electronphonon coupling and Schwinger pair production is an intrinsic graphene property that has not been investigated. Our motivation for studying clean graphene at low temperature is based on the following effect: for a fixed electric field, below a sufficiently low temperature linear eletric transport breaks down and nonlinear transport dominates. The criteria of the strength of this field [Fritz et al. (2008)] is eE = T2/~vF (1.1) For T >√eE~vF the system is in linear transport regime while for T <√eE~vF the system is in nonlinear transport regime. From the scaling’s point of view, at the nonlinear transport

BOOK REVIEWS: Quantum Mechanics: Fundamentals

NASA Astrophysics Data System (ADS)

Whitaker, A.

2004-02-01

Lamb shift. There is an interesting chapter on the physical interpretation of the Dirac equation, including such topics as the negative energy solutions, the Zitterbewegung and the Klein paradox. The last chapter in this part of the book is an extensive treatment of the symmetries and other properties of the Dirac equation, including the behaviour under rotation, translation, reflection, charge conjugation and time reversal. Helicity is explained, and the behaviour of zero-mass fermions is discussed; even though it now seems certain that neutrinos do not have zero-mass, this treatment provides a good approximation to their behaviour if they have high enough momenta. The last section on relativistic fields contains chapters on the quantization of relativistic fields, the free Klein--Gordon and Dirac fields, quantization of the radiation field, interacting fields and quantum electrodynamics, including the S matrix, Wick’s theorem and Feynman diagrams. Schwabl’s book would be excellent for those requiring a detailed presentation of the topics it includes, at a level of rigour appropriate to the physicist. It includes a substantial number of interesting problems. The third book under consideration, that by Gustafson and Sigal is very different from the others. In academic level, at least the initial sections may actually be slightly lower; the book covers a one-term course taken by senior undergraduates or junior graduate students in mathematics or physics, and the initial chapters are on basic topics, such as the physical background, basic dynamics, observables and the uncertainty principle. However the level of mathematical sophistication is far higher than in the other books. While the mathematical prerequisites are modest---real and complex analysis, elementary differential equations and preferably Lebesgue integration, a third of the book is made up of what are called mathematical supplements---on operator adjoints, the Fourier transform, tensor products, the