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arXiv · 2212.11965

Dimensional reduction of the Dirac equation in arbitrary spatial dimensions

Davide Lonigro·Rocco Maggi·Giuliano Angelone·Elisa Ercolessi·Paolo Facchi·Giuseppe Marmo·Saverio Pascazio·Francesco V. Pepe
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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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Davide Lonigro, Rocco Maggi, Giuliano Angelone, Elisa Ercolessi, Paolo Facchi, Giuseppe Marmo, Saverio Pascazio, Francesco V. Pepe. 2022-12-22. Dimensional reduction of the Dirac equation in arbitrary spatial dimensions. https://doi.org/10.1140/epjp/s13360-023-03919-0

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