Work

Coupled Proca theories: Green-hyperbolicity, quantization and applications to polarization measurement

Year: 2026

Type: article

Abstract: The Proca field describes a massive relativistic spin-1 particle and was originally formulated in Minkowski spacetime. Here we consider a variety of generalizations in globally hyperbolic spacetimes, including couplings between a number of Proca fields via a mass-matrix, the charged Proca field with arbitrary magnetic moment in an arbitrary external electromagnetic field, and a Proca–Klein–Gordon theory with a spacetime-dependent bilinear coupling. The equations are analysed using a general auxiliary field method, introduced here, which provides practical criteria for showing that a given operator is (semi)-Green-hyperbolic. The method goes beyond what is achieved in existing analyses of deformed equations, which for example place restrictions on the magnetic moment and electromagnetic potential that can be coupled to a Proca field. The theories considered can be quantized following a common pattern and all the examples treated in this work admit Hadamard states on any globally hyperbolic spacetime. As an application, the Proca–Klein–Gordon system is used to develop a measurement scheme sensitive to the Proca polarization, using a Klein–Gordon field as the probe. For a suitable family of n -particle Proca states, the leading-order probe response accords with Malus’ law, confirming that this system acts as a polarization-sensitive detector.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-026-01741-9

Authors: Christopher J. Fewster, Christiane K. M. Klein

Institution: University of York

Language: English

Topic: Quantum and Classical Electrodynamics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090