Dimensional reduction of the Dirac theory

Angelone G, Ercolessi E, Facchi P, Lonigro D, Maggi R, Marmo G, Pascazio S, Pepe FV (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Physics A: Mathematical and Theoretical Institute of Physics Publishing (IOP)

Book Volume: 56

Article Number: 065201

Journal Issue: 6

DOI: 10.1088/1751-8121/acb869

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.

Authors with CRIS profile

Davide Lonigro

Involved external institutions

University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro IT Italy (IT) Università degli Studi di Napoli Federico II IT Italy (IT) University of Bologna / Università di Bologna IT Italy (IT)

How to cite

APA:

Angelone, G., Ercolessi, E., Facchi, P., Lonigro, D., Maggi, R., Marmo, G.,... Pepe, F.V. (2023). Dimensional reduction of the Dirac theory. Journal of Physics A: Mathematical and Theoretical, 56(6). https://doi.org/10.1088/1751-8121/acb869

MLA:

Angelone, Giuliano, et al. "Dimensional reduction of the Dirac theory." Journal of Physics A: Mathematical and Theoretical 56.6 (2023).

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