Stochastic quantisation of scalar QFT on noncommutative spaces

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Abstract

We present a joint work with C. Song and H. Weber in which we treat the stochastic quantisation equation of the $\lambda\phi^4$ QFT model on 2-dimensional non-commutative Moyal space. We adapt the Da Prato--Debussche formulation to a matrix setting and corresponding spaces of distributions. Special care is necessary to estimate a mixed term which does not have a commutative analogue. We prove existence and uniqueness of the solution up to some small stochastic time and give an a priori estimate for large time. The tools from stochastic analysis then allow to deduce existence of an invariant measure. In the second part we outline our project to combine (1) stochastic quantisation, (2) the exact solution of the planar sector of $\lambda\phi^4$ model on 4-dimensional Moyal space and (3) free probabilty to construct an interacting QFT in four dimensions.

Speakers from the University of Münster

Wulkenhaar, Raimar

Professur für Reine Mathematik (Prof. Wulkenhaar)