协变Symanzik恒等式
Covariant Symanzik identities
摘要：
经典的同构定理，由于Dynkin，Eisenbaum，Le Jan和Sznitman建立之间的相关函数或分布的占用时间的随机路径或合奏的路径和马尔可夫场，如离散高斯自由场。我们扩展这些结果的情况下，真正的，复杂的，或四元数的任意秩的向量丛的图形赋予连接，通过提供分布之间的高斯自由向量场和holonomies的随机路径的泛函的身份。作为一个应用程序，我们给出了一个公式计算的时刻的一大类随机，在一般非高斯，领域的完整性方面的随机路径退火随机规范场，在精神的Symanzik的基础工作的主题。
英文摘要：
Classical isomorphism theorems due to Dynkin, Eisenbaum, Le Jan, and Sznitman establish equalities between the correlation functions or distributions of occupation times of random paths or ensembles of paths and Markovian fields, such as the discrete Gaussian free field. We extend these results to the case of real, complex, or quaternionic vector bundles of arbitrary rank over graphs endowed with a connection, by providing distributional identities between functionals of the Gaussian free vector field and holonomies of random paths. As an application, we give a formula for computing moments of a large class of random, in general non-Gaussian, fields in terms of holonomies of random paths with respect to an annealed random gauge field, in the spirit of Symanzik's foundational work on the subject.
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