English
Related papers

Related papers: On Dirac equations on phase spaces

200 papers

We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. We solve the difficulties…

General Relativity and Quantum Cosmology · Physics 2016-12-07 Christian J. Bordé , Jean-Claude Houard , Alain Karasiewicz

In this article, we studied the system of (2+1) dimensional Dirac equation in time-dependent noncommutative phase-space. Exactly, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method…

Quantum Physics · Physics 2020-05-08 Ilyas Haouam

Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…

High Energy Physics - Theory · Physics 2016-07-20 Giandomenico Palumbo

We present a new approach to study (1+1)-dimensional Dirac equation in the background of an effective mass $M$ by exploiting the possibility of a position-dependent fermi velocity $v_f$. We explore the resulting structure of the coupled…

Quantum Physics · Physics 2022-07-14 Rahul Ghosh

We use the polar decomposition to describe the Dirac field in terms of an effective spinorial fluid. After reformulating all covariant equations in ``spinorial'' signature $(+ -- )$, we develop a $(1+1+2)$ covariant approach for the Dirac…

General Relativity and Quantum Cosmology · Physics 2025-10-06 Stefano Vignolo , Giuseppe De Maria , Luca Fabbri , Sante Carloni

The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Semyon Pol'shin

Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…

General Relativity and Quantum Cosmology · Physics 2008-02-03 A. O. Barvinsky

We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices.…

General Relativity and Quantum Cosmology · Physics 2026-05-12 Stefano Vignolo , Giuseppe De Maria , Sante Carloni , Luca Fabbri

A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then…

Mathematical Physics · Physics 2011-09-13 V. M. Red'kov

Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product of C^{*}-algebras. Then we define the quantization of…

Symplectic Geometry · Mathematics 2014-10-10 Yanli Song

The Dirac equation has been studied in which the Dirac matrices $\hat{\boldmath$\alpha$}, \hat\beta$ have space factors, respectively $f$ and $f_1$, dependent on the particle's space coordinates. The $f$ function deforms Heisenberg algebra…

Quantum Physics · Physics 2009-11-11 I. O. Vakarchuk

We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…

High Energy Physics - Theory · Physics 2020-04-03 Ulf Lindström

We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…

Quantum Physics · Physics 2022-01-17 Bijan Bagchi , Rahul Ghosh

Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…

High Energy Physics - Theory · Physics 2008-11-26 Marcos Rosenbaum , J. David Vergara , L. Roman Juarez

Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…

High Energy Physics - Theory · Physics 2009-10-22 C. G. Torre

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…

Mathematical Physics · Physics 2024-11-13 Lawrence Frolov , Samuel E. Leigh , A. Shadi Tahvildar-Zadeh

We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.

Quantum Physics · Physics 2015-05-13 Dan Solomon

Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac-Euler equations for fermions involving a…

General Relativity and Quantum Cosmology · Physics 2022-10-12 Tonatiuh Matos , Omar Gallegos , Pierre-Henri Chavanis

We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…

High Energy Physics - Theory · Physics 2026-01-13 Omar Rodríguez-Tzompantzi

I present a review of the Dirac equation in general relativity. Although the generalization of the Dirac equation to a curved spacetime is well known, it is not usually part of the standard toolkit of techniques known to people working on…

General Relativity and Quantum Cosmology · Physics 2025-08-04 Miguel Alcubierre