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arXiv · 2207.03009

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

Mauricio Valenzuela·Jorge Zanelli
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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.

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Mauricio Valenzuela, Jorge Zanelli. 2022-07-06. On the spin content of the classical massless Rarita--Schwinger system. https://doi.org/10.21468/scipostphysproc.14.047

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