Dimensional reduction of the Dirac theory
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Published:2023-02-10
Issue:6
Volume:56
Page:065201
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ISSN:1751-8113
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Container-title:Journal of Physics A: Mathematical and Theoretical
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language:
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Short-container-title:J. Phys. A: Math. Theor.
Author:
Angelone GiulianoORCID,
Ercolessi Elisa,
Facchi PaoloORCID,
Lonigro DavideORCID,
Maggi Rocco,
Marmo GiuseppeORCID,
Pascazio SaverioORCID,
Pepe Francesco VORCID
Abstract
Abstract
We perform a reduction from three to two spatial dimensions of the physics of a spin-
1
2
fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical EM field, governed by the Dirac–Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an EM field provides a more complicated theory in
2
+
1
dimensions, in which the method of decent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.
Funder
Regione Puglia
Istituto Nazionale di Fisica Nucleare
European Union - NextGenerationEU
Italian National Group of Mathematical Physics
Ministero dell’Istruzione, dell’Università e della Ricerca
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference42 articles.
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