Dimensional reduction of the Dirac equation in arbitrary spatial dimensions

• URL: http://arxiv.org/abs/2212.11965v1
• Date: Thu, 22 Dec 2022 18:50:05 GMT
• Title: Dimensional reduction of the Dirac equation in arbitrary spatial dimensions
• Authors: Davide Lonigro, Rocco Maggi, Giuliano Angelone, Elisa Ercolessi, Paolo Facchi, Giuseppe Marmo, Saverio Pascazio, Francesco V. Pepe
• Abstract summary: We show that the Dirac equation reduces to either a single Dirac equation or two decoupled Dirac equations. We construct and discuss an explicit hierarchy of representations in which this procedure becomes manifest and can easily be iterated.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which consists in conceiving low-dimensional theories as a specialization of high-dimensional ones that are uniform along the additional space coordinate. We show that the Dirac equation reduces to either a single Dirac equation or two decoupled Dirac equations, depending on whether the higher-dimensional manifold has even or odd spatial dimensions, respectively. Furthermore, we construct and discuss an explicit hierarchy of representations in which this procedure becomes manifest and can easily be iterated.

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