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Quantization of counterexamples to Dirac’s conjecture

The European Physical Journal Plus volume 138, Article number: 939 (2023) Cite this article

Abstract

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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Acknowledgements

We thank F. Canfora for valuable discussions. This work was partially funded by grant FONDECYT 1220862.

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Authors and Affiliations

  1. Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastián, Valdivia, Chile

    Mauricio Valenzuela

  2. Centro de Estudios Científicos (CECs), Arturo Prat 514, Valdivia, Chile

    Mauricio Valenzuela

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  1. Mauricio Valenzuela
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Correspondence to Mauricio Valenzuela.

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Valenzuela, M. Quantization of counterexamples to Dirac’s conjecture. Eur. Phys. J. Plus 138, 939 (2023). https://doi.org/10.1140/epjp/s13360-023-04565-2

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