Quantization of counterexamples to Dirac's conjecture

• URL: http://arxiv.org/abs/2306.03080v2
• Date: Mon, 12 Jun 2023 18:22:50 GMT
• Title: Quantization of counterexamples to Dirac's conjecture
• Abstract summary: Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. We point out, however, that secondary first-class constraints are just initial conditions that do not imply Poisson's bracket modification. We apply the method to two Dirac's conjecture counterexamples, including Cawley's iconical system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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