Coupled Proca theories: Green-hyperbolicity, quantization and applications to polarization measurement
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866917080272470016 |
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| author | Fewster, Christopher J. Klein, Christiane K. M. |
| author_facet | Fewster, Christopher J. Klein, Christiane K. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coupled Proca theories: Green-hyperbolicity, quantization and applications to polarization measurement Fewster, Christopher J. Klein, Christiane K. M. Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Coupled Proca theories: Green-hyperbolicity, quantization and applications to polarization measurement |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.11348 |