发表机构
Departamento de Física, Universidad Nacional de Colombia; Facultad de Ciencias, Universidad Antonio Nariño（哥伦比亚国立大学物理系; 安东尼奥·纳里尼奥大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了规范非线性 sigma 模型的离壳 BRST 不变量子理论，利用 Killing 矢量实现几何解释，通过 BRST 上同调刻画物理态空间，并讨论了幺正性条件。
AI 中文摘要
我们构造了一个与非线性 sigma 模型耦合的非阿贝尔规范场的离壳 BRST 不变规范固定表述。从 GB 的动力学及其与规范场和鬼场的自洽耦合出发，我们构造了相应的 BRST 不变量子理论，并给出了关于 Killing 矢量的几何解释。我们处理的一个核心要点是，靶空间 Killing 矢量的李括号闭包提供了进入 BRST 微分的代数的几何实现。物理态空间由幂零 BRST 电荷的上同调来刻画，从而提供了物理与非物理自由度的自洽分离。我们明确推导了 BRST 电荷，并给出了相关的对称性变换。最后，我们分析了物理希尔伯特空间的结构，并讨论了 BRST 对称性支持幺正性并约束量子有效理论的条件。量子陈述以 BRST 保持的测度和正则化子为条件，四维模型被视为有效场论。
英文摘要
We construct an off-shell BRST-invariant gauge-fixed formulation of a nonlinear sigma model coupled to a non-Abelian gauge field. Starting from the dynamics of GBs and their consistent couplings to gauge and ghost fields, we construct the corresponding BRST-invariant quantum theory and provide a geometrical interpretation in terms of Killing vectors. A central point of our treatment is that the Lie-bracket closure of the target-space Killing vectors provides the geometric realization of the algebra entering the BRST differential. The physical state space is characterized by the cohomology of the nilpotent BRST charge, providing a consistent separation of physical and non-physical degrees of freedom. We explicitly derive the BRST charge and present the associated symmetry transformations. Finally, we analyze the structure of the physical Hilbert space and discuss the conditions under which BRST symmetry supports unitarity and constrains the quantum effective theory. Quantum statements are conditional on a BRST-preserving measure and regulator, and the four-dimensional model is treated as an effective field theory.
Comments19 pages, 1 figure
