On the spin content of the classical massless Rarita--Schwinger system
Abstract
We analyze the Rarita--Schwinger (RS) massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincar\'e group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture--that all first class constraints generate gauge symmetries--is assumed or not. In the affirmative case, a secondary first class constraint must be added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the spin-1/2 sector. In the opposite case, the spin-1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.
Keywords
Cite
@article{arxiv.2207.03009,
title = {On the spin content of the classical massless Rarita--Schwinger system},
author = {Mauricio Valenzuela and Jorge Zanelli},
journal= {arXiv preprint arXiv:2207.03009},
year = {2023}
}
Comments
11 pages. Further content related to the spin-1/2 projection of the RS action is included, references added and minor corrections in version 3. Based on talk given by MV at "Group 34" conference, Strasbourg University, 18-22 July 2022. Accepted in SciPost Physics Proceedings