Elliptic stochastic quantization of SinhGordon QFT
Abstract
The (elliptic) stochastic quantization equation for the (massive) $\cosh(\beta \varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\beta^2 < 4 \pi$), 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 OsterwalderSchrader axioms for the $\cosh (\beta \varphi)_2$ quantum field theory, including the exponential decay of correlation functions.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.12664
 Bibcode:
 2021arXiv210812664B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 60H17;
 81T08;
 81T40
 EPrint:
 Some typos have been corrected