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      Construction of the Gibbs measures associated with Euclidean quantum field theory with various polynomial interactions in the Wick renormalizable regime

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          Abstract

          In this paper, we consider the Gibbs measures associated with Euclidean quantum field theory with polynomial-type of interactions on the torus. We observe the (non-)normalizability of the multivariate version of \(P(\Phi)_2\) models by the variational method. Moreover, we extend this setting to the "fractional model" in the "Wick renormalizable regime": the base Gaussian measure has the inverse of the fractional power of the Laplacian as its covariance with the restriction that the Wick products that appear during the renormalization procedure are all well-defined. After working on the issue in a general setting, we also examine some specific examples as an application.

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          Author and article information

          Journal
          31 May 2023
          Article
          2305.19583
          ddc48aa3-6381-42dd-a753-3a032af2544f

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          81T08, 60H15
          42 pages
          math.PR

          Probability
          Probability

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