Stochastic quantization of the weighted exponential QFT
Seiichiro Kusuoka, Hirotatsu Nagoji

TL;DR
This paper establishes the existence and uniqueness of solutions to a stochastic quantization equation for a weighted exponential quantum field model on a 2D torus, addressing challenges posed by the drift term's sign variability.
Contribution
It introduces a novel approach to handle the stochastic quantization of the weighted exponential QFT, proving global solutions in the $L^2$-regime and linking them to a canonical Dirichlet form.
Findings
Proved unique existence of global solutions for the stochastic quantization equation.
Addressed the difficulty of sign-changing drift terms in the equation.
Connected the solutions to a Dirichlet form from the weighted exponential quantum field measure.
Abstract
We consider the stochastic quantization equation associated with the weighted exponential quantum field model (or the H{\o}egh-Krohn model) on the two dimensional torus. Unlike in the case of the usual (unweighted) exponential model, the drift term of the stochastic quantization equation can be both positive and negative, and that makes the equation more difficult to treat. We prove the unique existence of the time-global solution under a certain initial condition by a pathwise PDE argument in the so-called -regime. We also see that this solution is properly associated with a Dirichlet form canonically constructed from the weighted exponential quantum field measure.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Quantum Information and Cryptography · Advanced Mathematical Physics Problems
