Note on Gauge Invariance and Causal Propagation

Abstract

Interactions of gauge-invariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spin fields, the emphasis is usually put on gauge invariance that happens to be very selective by itself. We demonstrate with an explicit example, however, that gauge invariance, albeit indispensable for constructing interactions, may not suffice as a consistency condition. The chosen example that exhibits this feature is the theory of a massless spin-3/2 field coupled to electromagnetism. We show that this system admits an electromagnetic background in which the spin-3/2 gauge field may move faster than light. Requiring causal propagation rules out otherwise allowed gauge-invariant couplings. This emphasizes the importance of causality analysis as an independent test for a system of interacting gauge fields. We comment on the implications of allowing new degrees of freedom and non-locality in a theory, on higher-derivative gravity and Vasiliev's higher-spin theories.

11 pages, to appear in PRD, comments and references added

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Cited by in corpus (11)

• Massive Gravity
• From Higher Spins to Strings: A Primer
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Acausality and Nonunique Evolution in Generalized Teleparallel Gravity
• Causality Constraints on Massive Gravity
• Eikonal Scattering and Asymptotic Superluminality of Massless Higher Spin Fields
• Massive Higher Spin Fields Coupled to a Scalar: Aspects of Interaction and Causality
• Higher-Spin States of the Superstring in an Electromagnetic Background
• Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• The Involutive System of Higher-Spin Equations