Quantization of counterexamples to Dirac’s conjecture

Valenzuela, Mauricio

doi:10.1140/epjp/s13360-023-04565-2

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2024

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“…Consequently, it is proposed to assume the validity of the DC as a general rule [55]. However, it has been shown that quantizing first and then restricting to the surface of secondary first-class constraints avoids these obstructions [82]. Furthermore, in fermionic systems, such as the one that concerns us here, the Dirac bracket is symmetric in Grassmann-odd variables and the constraints are self-conjugate [83].…”

Section: Discussion and Summarymentioning

confidence: 99%

Massless Rarita-Schwinger equations: Half and three halves spin solution

Valenzuela,

Zanelli

2024

SciPost Phys.

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Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -free of arbitrary functions of time- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-1/2 mode via the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.

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Section: Discussion and Summarymentioning

confidence: 99%