晶格杨-米尔斯有限 N 主环方程的新推导

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2024-01-01 DOI:10.1214/24-ejp1090

Hao Shen, Scott A. Smith, Rongchan Zhu

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引用次数: 0

摘要

.我们给出了结构群为 SO ( N ) 、U ( N ) 或 SU ( N ) 的晶格杨-米尔斯理论的非 N 主环方程的新推导。SO ( N ) 的情况最初由查特吉在[Cha19a]中证明，而 SU ( N ) 则由贾法洛夫在后续工作[Jaf16]中分析。我们的方法基于朗之文动态，即构型流形上的 SDE，并通过伊特奥公式得到了简单的证明。

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A new derivation of the finite N master loop equation for lattice Yang-Mills

. We give a new derivation of the ﬁnite N master loop equation for lattice Yang-Mills theory with structure group SO ( N ), U ( N ) or SU ( N ). The SO ( N ) case was initially proved by Chatterjee in [Cha19a], and SU ( N ) was analyzed in a follow-up work by Jafarov [Jaf16]. Our approach is based on the Langevin dynamic, an SDE on the manifold of conﬁgurations, and yields a simple proof via Itˆo’s formula.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.