https://doi.org/10.1140/epjp/s13360-023-04565-2
Regular Article
Quantization of counterexamples to Dirac’s conjecture
1
Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastián, Valdivia, Chile
2
Centro de Estudios Científicos (CECs), Arturo Prat 514, Valdivia, Chile
Received:
29
June
2023
Accepted:
5
October
2023
Published online:
23
October
2023
Dirac’s conjecture, that secondary first-class constraints generate transformations that do not change the physical system’s state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be defined, and restricting the phase space first and then quantizing is an inconsistent procedure. The latter observation has discouraged the study of systems of this kind more profoundly, while Dirac’s conjecture is assumed generally valid. We point out, however, that secondary first-class constraints are just initial conditions that do not imply Poisson’s bracket modification, and we carry out the quantization successfully by imposing these constraints on the initial state of the wave function. We apply the method to two Dirac’s conjecture counterexamples, including Cawley’s iconical system.
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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.
