English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the Gibbs measures associated with Euclideanquantum field theory with polynomial-type of interactions on the torus. Weobserve 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 Gaussianmeasure has the inverse of the fractional power of the Laplacian as itscovariance with the restriction that the Wick products that appear during therenormalization procedure are all well-defined. After working on the issue in ageneral setting, we also examine some specific examples as an application.

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