https://doi.org/10.1140/epjp/s13360-023-04285-7
Regular Article
Single-particle quantum mechanics of the free Klein–Gordon equation with Lorentz violation
Department of Physics and Astronomy, University of South Carolina, 29208, Columbia, SC, USA
Received:
30
November
2022
Accepted:
14
July
2023
Published online:
24
July
2023
In spite of its problems with interactions, the first-quantized Klein–Gordon equation is a satisfactory theory of free spinless particles. Moreover, the usual theory may be extended to describe Lorentz-violating behavior, of the same types that exist can in second-quantized scalar field theories. However, because the construction of the theory requires a restriction to positive-energy modes, the Hilbert space inner product and the position operator depend explicitly on the form of the Lorentz violation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
