具有普适额外维的Yang-Mills理论的Batalin-Vilkovisky描述
Batalin-Vilkovisky description of Yang-Mills theories with universal extra dimensions
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中文总结 AI 辅助
本文利用Batalin-Vilkovisky框架构造具有普适额外维的纯Yang-Mills理论的BRST不变扩展作用量，通过正则变换隐藏高维对称性，并协变固定标准与KK场，强调量子化理论的显式SU(N)规范对称性。
中文摘要 AI 辅助
Batalin-Vilkovisky（BV）框架是量子化各种规范系统的强大技术。该形式体系利用场和反场——通过反括号引入辛结构——来实现BRST对称性，后者捕捉了规范不变性的本质。在此背景下，我们研究了具有普适额外维的纯Yang-Mills理论的对称性结构。我们为$(4+n)$维理论构造了一个依赖于场和反场的BRST不变扩展作用量，该作用量构成主方程的一个恰当解。高维时空和规范对称性随后通过正则变换隐藏在其四维对应物中。规范不变性通过结合标准场和Kaluza-Klein（KK）场的规范固定程序来固定。该程序在规范群的伴随表示中协变地实现。标准规范场使用背景场方法（BFM）固定，而KK规范激发态则协变地固定，因为它们作为物质场变换。最后，强调了量子化理论的显式$SU(N)$规范对称性。
英文摘要
The Batalin-Vilkovisky (BV) framework is a powerful technique for quantizing a wide range of gauge systems. This formalism employs fields and antifields--introducing a symplectic structure through the antibracket--to implement BRST symmetry, which captures the essence of gauge invariance. Within this context, we study the symmetry structure of a pure Yang-Mills theory with universal extra dimensions. We construct a BRST-invariant extended action for the $(4+n)$-dimensional theory depending on fields and antifields, which constitutes a proper solution to the master equation. The higher-dimensional spacetime and gauge symmetries are then hidden within their four-dimensional counterparts via canonical transformations. Gauge invariances are fixed by combining gauge-fixing procedures for both the standard and Kaluza-Klein (KK) fields. This procedure is implemented covariantly in the adjoint representation of the gauge group. While the standard gauge fields are fixed using the Background Field Method (BFM), the KK gauge excitations are fixed covariantly, as they transform as matter fields. Finally, the manifest $SU(N)$ gauge symmetry of the quantized theory is emphasized.
发表机构
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理与数学科学学院）
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