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On the spin content of the classical massless Rarita-Schwinger system

Mauricio Valenzuela, Jorge Zanelli

SciPost Phys. Proc. 14, 047 (2023) · published 24 November 2023

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34th International Colloquium on Group Theoretical Methods in Physics


We analyze the Rarita-Schwinger massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a 1/2 and a 3/2 propagating Poincaré group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture is assumed or not. In the affirmative case, a secondary first class constraint is added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the 1/2 sector. In the opposite case, the 1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

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