https://doi.org/10.1140/epjp/s13360-023-03919-0
Regular Article
Dimensional reduction of the Dirac equation in arbitrary spatial dimensions
1
Dipartimento di Fisica, Università di Bari, 70126, Bari, Italy
2
INFN, Sezione di Bari, 70126, Bari, Italy
3
Dipartimento di Fisica e Astronomia, Università di Bologna, 40127, Bologna, Italy
4
INFN, Sezione di Bologna, 40127, Bologna, Italy
5
Dipartimento di Fisica, Università di Napoli Federico II, 80126, Naples, Italy
6
INFN, Sezione di Napoli, 80126, Naples, Italy
Received:
23
January
2023
Accepted:
20
March
2023
Published online:
8
April
2023
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.
© The Author(s) 2023
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