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Related papers: New explicit expressions for Dirac bilinears

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We study the Maxwell-Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The…

Mathematical Physics · Physics 2015-06-19 Shaun Inglis , Peter Jarvis

Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is…

General Physics · Physics 2008-02-21 Geoffrey F. Chew

We consider the theory of spinor fields written in polar form and we re-express it in terms of the so-called 1+1+2 covariant splitting: after this is done for the basic kinematic variables, we proceed to decompose the dynamical equations,…

Mathematical Physics · Physics 2025-07-24 Luca Fabbri , Stefano Vignolo , Giuseppe De Maria , Sante Carloni

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in…

Quantum Physics · Physics 2009-11-10 Jens Bolte , Rainer Glaser

Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…

Quantum Physics · Physics 2016-10-12 Taeseung Choi , Sam Young Cho

We obtain the affine Euler-Poincar\'e equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin…

Chaotic Dynamics · Physics 2009-04-10 F. Gay-Balmaz , D. D. Holm , T. S. Ratiu

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

Part I: The geometric algebra of space is derived by extending the real number system to include three mutually anticommuting square roots of plus one. The resulting geometric algebra is isomorphic to the algebra of complex 2x2 matrices,…

Mathematical Physics · Physics 2015-07-24 Garret Sobczyk

We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton…

Mathematical Physics · Physics 2009-11-10 A. D. Alhaidari

The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and…

Quantum Physics · Physics 2025-12-23 Thiago T. Tsutsui , Alison A. Silva , Antonio S. M. de Castro , Fabiano M. Andrade

We initiate the construction of the global Poincar\'e algebra generators in the context of the post-Minkowskian Hamiltonian formulation of gravitating binary dynamics in isotropic coordinates that is partly inspired by scattering…

General Relativity and Quantum Cosmology · Physics 2023-06-06 Hojin Lee , Sangmin Lee

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

We show a nice symmetric/antisymmetric relation between the four vector Lorentz transformation and the Dirac spinor one in the Majorana representation. From the spinor one, we exhibit the antisymmetric pending of the symmetric Minkowski…

General Physics · Physics 2023-04-10 Guy Barrand

As previously shown, the special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz boosts and rotations. This insight indicate that the…

Mathematical Physics · Physics 2011-06-08 J. Buitrago , S. Hajjawi

We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…

High Energy Physics - Theory · Physics 2014-11-18 Roberto Casalbuoni , Joaquim Gomis , Kiyoshi Kamimura , Giorgio Longhi

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under…

High Energy Physics - Theory · Physics 2015-06-12 J. M. Hoff da Silva , Roldão da Rocha

The phenomenon of spin-dependent quantum scattering in two-dimensional (2D) pseudospin-1/2 Dirac materials leading to a relativistic quantum chimera was recently uncovered. We investigate spin-dependent Dirac electron optics in 2D…

Mesoscale and Nanoscale Physics · Physics 2024-08-23 Li-Li Ye , Chen-Di Han , Ying-Cheng Lai

We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both $\Gamma$\,-matrices and the relativistic spin tensor are produced through the canonical quantization…

High Energy Physics - Theory · Physics 2015-05-28 A. A. Deriglazov

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences {\it Zitterbewegung},…

High Energy Physics - Theory · Physics 2015-05-28 A. A. Deriglazov

The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4+4)-space. Split octonionic representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form are explicitly…

Mathematical Physics · Physics 2023-08-22 Merab Gogberashvili , Alexandre Gurchumelia