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Related papers: Comments on "Dirac theory in spacetime algebra"

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Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…

Quantum Physics · Physics 2016-05-11 R. Vilela Mendes

In this paper using the apparatus of the Clifford bundle formalism we show how straightforwardly solve in Minkowski spacetime the Dirac-Hestenes equation -- which is an appropriate representative in the Clifford bundle of differential forms…

Mathematical Physics · Physics 2007-05-23 Roldao da Rocha , Waldyr A. Rodrigues

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for…

General Relativity and Quantum Cosmology · Physics 2010-11-23 Vladimir V. Kassandrov

It is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac-Hestenes equation instead of a complex solution to the Dirac equation. The current research presents a formulation of the…

Mathematical Physics · Physics 2025-06-10 S. V. Rumyantseva , D. S. Shirokov

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions…

General Relativity and Quantum Cosmology · Physics 2014-11-20 Mayeul Arminjon , Frank Reifler

Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute…

Quantum Physics · Physics 2007-05-23 Yuri A. Rylov

We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…

High Energy Physics - Theory · Physics 2014-04-21 V. G. Kupriyanov

Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.

Mathematical Physics · Physics 2019-06-21 Volodymyr Sushch

The Poincare and Poincare-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypothesizes concerning…

General Relativity and Quantum Cosmology · Physics 2016-11-01 O. V. Babourova , B. N. Frolov , P. E. Kudlaev , E. V. Romanova

We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…

Mathematical Physics · Physics 2026-02-18 Muzaffer Adak , Ali Bagci , Caglar Pala , Ozcan Sert

We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all…

High Energy Physics - Phenomenology · Physics 2013-03-11 U. D. Jentschura , B. J. Wundt

We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we…

Mathematical Physics · Physics 2023-01-18 Vaclav Zatloukal

This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Mihalis Dafermos

A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_\mu dx^\mu$ is left invariant under the symmetry group…

High Energy Physics - Theory · Physics 2009-01-28 C. A. Dartora , G. G. Cabrera

Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Mayeul Arminjon

Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Ugur Camci

Based on experimental evidences supporting the hypothesis that neutrinos might be spacelike particles, a new Dirac-type equation is proposed and a spin-1/2 spacelike quantum theory is developed. The new Dirac-type equation provides a…

Quantum Physics · Physics 2007-05-23 Tsao Chang

The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…

Quantum Physics · Physics 2009-11-07 G. N. Ord

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field.…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Frank Reifler , Randall Morris

The application of the theory of scale relativity to microphysics aims at recovering quantum mechanics as a new non-classical mechanics on a non-derivable space-time. This program was already achieved as regards the Schr\"odinger and Klein…

High Energy Physics - Theory · Physics 2008-11-26 Marie-Noelle Celerier , Laurent Nottale