Zitterbewegung and semiclassical observables for the Dirac equation

Bölte, Jens; Glaser, Rainer

doi:10.1088/0305-4470/37/24/012

Cited by 15 publications

(8 citation statements)

References 28 publications

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“…11] for details. Generalisation of Gutzwiller's work for spin Dirac operators on Minkowski spacetime is due to Bolte and Keppeler [9,10] (see also the elucidating articles [7,8] and references therein for chronological developments). In contemporary to their reports, mathematical rigour analysis has been reported by Sandoval [40] promoting the Duistermaat-Guillemin framework for Diractype operators on a closed Riemannian manifold.…”

Section: Weyl Lawmentioning

confidence: 99%

A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

Islam¹

2021

Preprint

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A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on a globally hyperbolic spatially compact standard stationary spacetime is achieved by generalising the recent construction by A. Strohmaier and S. Zelditch [Adv. Math. 376, 107434 (2021)] to a vector bundle setting. We have analysed the spectrum of the Lie derivative with respect to the Killing vector field on the solution space of the Dirac equation and found that it consists of discrete real eigenvalues. The distributional trace of the Cauchy evolution operator has singularities at the periods of induced Killing flow on the space of lightlike geodesics. This gives rise to the Weyl law asymptotic at the vanishing period.1 We do not require Einstein's field equations to be satisfied.2 Global existence of a Lorentz metric depends on the topology of M . In particular, such a metric exists in all non-compact manifolds and compact manifolds with vanishing Euler characteristics. 3A spin-structure always exists locally but its global existence depends on some higher orientability property of the base manifold. For example, spin c and spin structures exist if and only if the third integral and the second Stiefel-Whitney class of spacetime vanish, respectively.

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Section: Weyl Lawmentioning

confidence: 99%

A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

Islam¹

2021

Preprint

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“…Despite the experimental circumstances not being favorable to such an interpretation, the quantum transitions that produces a final flavor state corresponding to an active-sterile quantum mixing is perfectly acceptable from the theoretical point of view. Even focusing specifically on the chiral oscillation mechanism, we have also observed a generic interest in identifying the physical meaning of variables which coexist with the interference between positive and negative frequency solutions of Dirac equation[89][90][91][92] in a Dirac wave packet treatment. If we follow an almost identical line of reasoning as that applied for rapid oscillations of the position, it is also possible to verify that the average value of the Dirac chiral operator γ 5 also presents an oscillating behavior.We intend to clarify some conceptual relations between helicity and chirality by constructing the dynamics of the processes of chiral oscillation and spin-flipping.…”

mentioning

confidence: 99%

Quantum flavor oscillations extended to the Dirac theory

Bernardini

Guzzo²,

Nishi

2011

Fortschritte der Physik

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This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first and second quantization theories. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass-eigenstates since in the standard treatment of oscillations the mass-eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac-type particle. The left-handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. The conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations.Comment: 116 pages, 10 figures (The abstract was suppressed due to online title limitations of the abstract field. See the manuscript for obtaining the complete abstract

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“…For the corresponding relativistic program to be carried out, the state for a spin 1/2 particle must have a simi-arXiv:1805.08243v1 [quant-ph] 21 May 2018 lar representation in the quantum and classical realms. Since spinors represent quantum states, the spinorial formulation of classical mechanics is desired [45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Operational dynamical modeling of spin 1/2 relativistic particles

Cabrera

Campos

Rabitz

et al. 2019

Eur. Phys. J. Spec. Top.

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The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. 109, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic Ehrenfest theorems by assuming that the coordinates and momenta do not commute. Forbidding creation of antiparticles and requiring the commutativity of the coordinates and momenta lead to classical Spohn's equation [Ann. Phys. 282, 420 (2000)]. Moreover, Spohn's equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.

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Zitterbewegung and semiclassical observables for the Dirac equation

Cited by 15 publications

References 28 publications

A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

A Gutzwiller Trace formula for Dirac Operators on a Stationary Spacetime

Quantum flavor oscillations extended to the Dirac theory

Operational dynamical modeling of spin 1/2 relativistic particles

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