Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus
Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus
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DOI：
10.2422/2036-2145.202105_106
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
S. Albeverio;Hiroshi Kawabi;Stefan-Radu Mihalache;M. Roeckner
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文献类型：
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作者：
S. Albeverio;Hiroshi Kawabi;Stefan-Radu Mihalache;M. Roeckner
我们考虑具有指数/三角相互作用的时空量子场。在欧几里德量子场论中，前者和后者分别被称为Hoegh-Krohn模型和Sine-Gordon模型。本文的主要目的是构造无限维扩散过程，利用Dirichlet形式方法求解二维环面上这些量子场的修正随机量子化方程，并证明相应Dirichlet算子的强唯一性.
We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Hoegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.