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arXiv 1710.02494hep-thgr-qc
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杨-米尔斯理论的规范不变场和流动方程

Gauge-invariant fields and flow equations for Yang-Mills theories

C. Wetterich

摘要:

本文讨论了非阿贝尔规范理论的规范不变场的概念。给定规范场周围的无穷小涨落可以分为物理涨落和规范涨落。从某个参考场出发,通过连续叠加物理涨落,构造规范不变场。任意的规范场都可以映射到相应的规范不变场。一个依赖于规范不变场的有效作用量通过将每个规范场与相应的规范不变场相关联而成为任意规范场的规范不变泛函。规范不变的有效作用量可以从一个隐式泛函积分与适当的“物理规范固定“得到。我们将这个概念推广到规范不变的有效平均行动或流动行动,其中涉及红外截止。它服从规范不变的泛函流方程。我们演示了使用这个流动方程的一个简单的计算纯$SU(N)$ -杨米尔斯理论中的运行规范耦合和传播子。

英文摘要:

We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical fluctuations. An arbitrary gauge field can be mapped to an associated gauge invariant field. An effective action that depends on gauge-invariant fields becomes a gauge-invariant functional of arbitrary gauge fields by associating to every gauge field the corresponding gauge-invariant field. The gauge-invariant effective action can be obtained from an implicit functional integral with a suitable "physical gauge fixing". We generalize this concept to the gauge-invariant effective average action or flowing action, which involves an infrared cutoff. It obeys a gauge-invariant functional flow equation. We demonstrate the use of this flow equation by a simple computation of the running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory.

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