zeta正则化行列式的圈汤表示与等变Symanzik恒等式
Loop soup representation of zeta-regularised determinants and equivariant Symanzik identities
AI总结：
本文推导了流形上向量丛拉普拉斯型算子行列式的随机表示（逆幂为布朗圈汤和乐乘积的期望，适用于2/3维紧致流形），并得出连续性、共形不变性等推论，还构造了最小耦合标量场并证明其满足Symanzik恒等式。
摘要：
我们推导了流形上向量丛拉普拉斯型算子行列式的随机表示：这些行列式的逆幂可表示为布朗圈汤定义的和乐乘积的期望。结果适用于2或3维紧致流形（含质量项或边界），并得出若干推论，包括行列式作为算子函数的连续性，以及曲面上行列式的共形不变性。该表达式可构造与给定随机光滑规范场最小耦合的标量场，证明其满足Symanzik恒等式；部分结果是A. Kassel和T. Lévy离散工作的连续类比。
英文摘要：
We derive a stochastic representation for determinants of Laplace-type operators on vectors bundles over manifolds. Namely, inverse powers of those determinants are written as the expectation of a product of holonomies defined over Brownian loop soups. Our results hold over compact manifolds of dimension 2 or 3, in the presence of a mass or a boundary. We derive a few consequences, including some continuity of these determinants as a function of the operator, and the conformal invariance of the determinant on surfaces. This expression allows us to construct the scalar field minimally coupled to a prescribed random smooth gauge field, which we prove obeys the so-called Symanzik identities. Some of these results are continuous analogues of the work of A. Kassel and T. Lévy in the discrete.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
