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arXiv · 2502.02355

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

Chunqiu Song·Hendrik Weber·Raimar Wulkenhaar
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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 $\lambda$.

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Chunqiu Song, Hendrik Weber, Raimar Wulkenhaar. 2025-02-04. Stochastic quantization of $\lambda \phi_2^4$- theory in 2-d Moyal space. https://arxiv.org/abs/2502.02355

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