Stochastic quantization of $\lambda \phi_2^4$- theory in 2-d Moyal space

TL;DR

This paper develops a stochastic quantization approach for the two-dimensional non-commutative $3bb$ theory on Moyal space, establishing well-posedness and constructing the associated quantum measure.

Contribution

It introduces a stochastic quantization method for the 2D Moyal $3bb$ model and proves well-posedness, advancing non-perturbative construction techniques.

Findings

Proved local and global well-posedness of the stochastic quantization equation.

Constructed the Moyal $3bb$ measure for any non-negative coupling.

Established a foundation for non-perturbative analysis of non-commutative QFTs.

Abstract

There is strong evidence for the conjecture that the $\lambda \phi^4$ QFT- model on 4-dimensional non-commutative Moyal space can be non-perturbatively constructed. As preparation, in this paper we construct the 2-dimensional case with the method of stochastic quantization. We show the local well-posedness and global well-posedness of the stochastic quantization equation, leading to a construction of the Moyal $\lambda \phi^4_2$ measure for any non-negative coupling constant $\lambda$.