2021/08/28 by Nikolay A. Barashkov, Barashkov, Nikolay, Francesco C. De Vecchi +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H17 #81T08 #81T40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2108.12664
openalex publication_date 2021/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The (elliptic) stochastic quantization equation for the (massive) \cosh(βφ)2 model, for the charged parameter in the L2 regime (i.e. β2 < 4 π), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the \cosh (βφ)2 quantum field theory, including the exponential decay of correlation functions.