Dimensional reduction of the Dirac theory. (10th February 2023)

• Record Type: Journal Article
• Authors: Angelone, Giuliano; Ercolessi, Elisa; Facchi, Paolo; Lonigro, Davide; Maggi, Rocco; Marmo, Giuseppe; Pascazio, Saverio; Pepe, Francesco V
• Is Part Of: Journal of physics. Volume 56:Number 6(2023)
• Publication Date: 2023-02-10
• Subjects: dimensional reduction -- Hadamard's descent -- Dirac equation -- Dirac–Maxwell equation -- low-dimensional theories; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/acb869
• Languages: English
• ISSNs: 1751-8113

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.