论文标题
Abelian Higgs模型的量规场边缘
Gauge field marginal of an Abelian Higgs model
论文作者
论文摘要
我们研究了Abelian Higgs模型的量规场边缘，该模型具有在有限体积的2D晶格上定义的反派动作。我们的第一个主要结果是在任意有限图上的量规理论，并且不认为结构组是Abelian，是radon的循环扩展 - 相对于纯仪表理论的规格场法则的nikodym衍生物。这种扩展类似于Seiler之一，但具有更大的通用性，并使用了不同的图理论方法。此外，我们显示了固定规格中该模型的量规场的紫外线稳定性。更具体地说，我们表明，在Arxiv：1808.09196中引入的H {Ö} lder--Besov型规范的矩在晶格间距中均匀地界定。后一个结果依赖于定量磁管不平等，而高斯随机变量的循环膨胀和基本特性又依靠。
We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on arbitrary finite graphs and does not assume that the structure group is Abelian, is a loop expansion of the Radon--Nikodym derivative of the law of the gauge field marginal with respect to that of the pure gauge theory. This expansion is similar to the one of Seiler but holds in greater generality and uses a different graph theoretic approach. Furthermore, we show ultraviolet stability for the gauge field marginal of the model in a fixed gauge. More specifically, we show that moments of the H{ö}lder--Besov-type norms introduced in arXiv:1808.09196 are bounded uniformly in the lattice spacing. This latter result relies on a quantitative diamagnetic inequality that in turn follows from the loop expansion and elementary properties of Gaussian random variables.
