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

by Mauricio Valenzuela and Jorge Zanelli

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Mauricio Valenzuela
Submission information
Preprint Link: scipost_202211_00048v2  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-01-24 19:09
Submitted by: Valenzuela, Mauricio
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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 spin-1/2 and a spin-3/2 propagating Poincare 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 spin-1/2 sector. In the opposite case, the spin-1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

Author comments upon resubmission

We have added the reference by W. Heidenreich, J. Math. Phys. 27 (1986) 2154-2159.

List of changes

In section 4, Conclusions, page 7, we added the second paragraph, which reads:

"As for quantization issues, the \tralf sector of the massless RS field has been quantized in various approaches \cite{Senjanovic:1977vr,Pilati:1977ht,Fradkin:1977wv}. In all of them, both \half sectors of the Poincar\'e group decomposition are factored out. Following reference \cite{Heidenreich:1986vx}---where it is shown that the massless RS field decomposes in a \half (pure gauge) sector with 0-norm, and \half and \tralf sectors of positive norm---the massless RS can be quantized \`a la Gupta-Bleuler factoring out only the zero norm state."

which includes the new reference

{\it On solutions spaces of massless field equations with arbitrary spin}, J. Math. Phys. \textbf{27} (1986), 2154-2159

added to the bibliography list as item [31].

Published as SciPost Phys. Proc. 14, 047 (2023)

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