阿贝尔规范理论的随机量子化
Stochastic quantization of an Abelian gauge theory
摘要：
本文研究了环面上U（1）格点规范理论的朗之万动力学，证明了在适当的规范下，朗之万动力学短时间收敛到时空白噪声驱动的随机偏微分方程系统.这也产生了收敛的一些规范不变的可观的短时间间隔。我们通过DeTurck技巧固定规范，并证明了一个版本的沃德恒等式，该恒等式导致取消重整化常数，否则会破坏规范对称性。证明依赖于离散版本的规律性结构理论。
英文摘要：
We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant observables on a short time interval. We fix gauge via a DeTurck trick, and prove a version of Ward identity which results in cancellation of renormalization constants that would otherwise break gauge symmetry. The proof relies on a discrete version of the theory of regularity structures.
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