Classical and Quantum Gauged Massless Rarita-Schwinger Fields

Abstract

We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields consistent classical and quantum theories, with a generalized fermionic gauge invariance. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. The quantized case is studied in gauge covariant radiation gauge and ${\Psi }_0=0$ gauge for the Rarita-Schwinger field, by both functional integral and Dirac bracket methods. In ${\Psi }_0=0$ gauge, the constraints have the form needed to apply the Faddeev-Popov method for deriving a functional integral. The Dirac bracket approach in ${\Psi }_0=0$ gauge yields consistent Hamilton equations of motion, and in covariant radiation gauge leads to anticommutation relations with the correct positivity properties. We discuss relativistic covariance of the anticommutation relations, and of Rarita-Schwinger scattering from an Abelian potential. We note that fermionic gauge transformations are a canonical transformation, but further details of the transformation between different fermionic gauges are left as an open problem.

Latex, 54 pages. Revised and expanded; in v2, positivity of the anticommutator is shown in covariant radation gauge; in v3, role of Ψ_0=0 gauge is discussed; in v4, many edits and Secs. 3 and 11 are new. Following v4, this paper has been rewritten and split into two papers: arXiv:1508.03380 and arXiv:1508.03382

References in corpus (3)

• Universal Limits on Massless High-Spin Particles
• Higher-spin massless S-matrices in four-dimensions
• SU(8) family unification with boson-fermion balance

Cited by in corpus (16)

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• Chiral Anomaly Calculation in the Extended Coupled Rarita-Schwinger Mode
• Gravitational chiral anomaly for spin 3/2 field interacting with spin 1/2 field
• Coleman-Weinberg symmetry breaking in $SU(8)$ induced by a third rank antisymmetric tensor scalar field
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• Anomalous transport from geometry
• Spin-1/2 and spin-3/2 field solutions in plane wave spacetimes
• On the photon mass generation in Rarita-Schwinger QED
• Chiral spin-3/2 particles in a medium
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