耦合Proca理论：格林双曲性、量子化及其在偏振测量中的应用
Coupled Proca theories: Green-hyperbolicity, quantization and applications to polarization measurement
AI总结：
本文研究全局双曲时空中多类耦合Proca理论，提出通用辅助场方法给出格林双曲性判据，实现统一量子化，并基于Proca-Klein-Gordon系统设计了符合马吕斯定律的Proca偏振探测方案。
摘要：
Proca场描述有质量相对论性自旋为1的粒子，最初是在闵可夫斯基时空中构建的。本文研究全局双曲时空中的多类Proca场推广形式，包括多个Proca场通过质量矩阵实现的耦合、处于任意外部电磁场中具有任意磁矩的带电Proca场，以及含时空依赖双线性耦合项的Proca-Klein-Gordon理论。本文提出一种通用辅助场方法分析相关场方程，该方法可给出判定给定算子为（半）格林双曲算子的实用判据，突破了现有变形方程分析的局限——现有研究例如会对可与Proca场耦合的磁矩、电磁势施加限制。本文研究的各类理论均可遵循统一模式完成量子化，且文中处理的所有示例在任意全局双曲时空中都存在哈达玛态。作为应用，本文利用Proca-Klein-Gordon系统设计了对Proca偏振敏感的测量方案，以Klein-Gordon场作为探针；对于合适的n粒子Proca态族，探针的领头阶响应符合马吕斯定律，证实该系统可作为偏振敏感探测器。
英文摘要：
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.
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