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Stochastic quantization of $λφ_2^4$- theory in 2-d Moyal space
Chunqiu Song, Hendrik Weber, Raimar Wulkenhaar · 2025-02-04 · via math.PR updates on arXiv.org

There is strong evidence for the conjecture that the $λφ^4$ 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 $λφ^4_2$ measure for any non-negative coupling constant $λ$.

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