发表机构
The Ohio State University（俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以双粒子一维平移不变系统为例，教学式展示BRST量子化作为核多体系统中恢复破缺对称性的投影方法替代方案，涵盖哈密顿量与路径积分表述及零模处理。
AI 中文摘要
我们提出了一个BRST量子化的教学展示，用于在核多体系统中恢复对称性，作为传统投影方法的重构和潜在替代方案。该形式体系通过一维中两个相互作用质量组成的简单系统的平移不变性加以说明，但着眼于推广到更多粒子、更高维度及其他对称性。我们解释了BRST构造中特定选择背后的考量，并发展了哈密顿量和路径积分两种表述，为各种多体和有效场论背景下可能有益于对称性恢复的规范固定提供指导。对于演示系统，我们展示了如何在扩展的BRST相空间中对角化，如何对乘积参考态恢复投影后变分，如何构造相应的规范固定泛函积分，以及如何隔离和控制集体零模。自始至终，我们牢记将BRST对称性扩展到各种近似方案，作为一致对称性恢复的指南。
英文摘要
We present a pedagogical showcase of BRST quantization for restoring symmetries in nuclear many-body systems as a reformulation and potential alternative to conventional projection methods. The formalism is illustrated using translational invariance for a simple system of two interacting masses in one dimension, but with an eye toward generalizing to more particles, higher dimensions, and other symmetries. We explain the considerations underlying particular choices within the BRST construction, and develop both Hamiltonian and path integral formulations to provide guidance for the variety of many-body and effective field theory contexts where gauge fixing for symmetry restoration might be useful. For the demonstration system we show how to diagonalize within the extended BRST phase space, how variation after projection is recovered for product reference states, how the corresponding gauge-fixed functional integral is constructed, and how collective zero modes are isolated and controlled. Throughout, we keep in mind extensions of BRST symmetry to various approximation schemes as a guide for consistent symmetry restoration.
Comments44 pages, 7 figures. Updated acknowledgements
