Quasi regular Dirichlet forms and the stochastic quantization problem

Sergio Albeverio; Zhi Ming Ma; Michael Röckner

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arXiv · 1404.2757

Quasi regular Dirichlet forms and the stochastic quantization problem

Sergio Albeverio·Zhi Ming Ma·Michael Röckner

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Abstract

After recalling basic features of the theory of symmetric quasi regular Dirichlet forms we show how by applying it to the stochastic quantization equation, with Gaussian space-time noise, one obtains weak solutions in a large invariant set. Subsequently, we discuss non symmetric quasi regular Dirichlet forms and show in particular by two simple examples in infinite dimensions that infinitesimal invariance, does not imply global invariance. We also present a simple example of non-Markov uniqueness in infinite dimensions.

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Sergio Albeverio, Zhi Ming Ma, Michael Röckner. 2014-04-10. Quasi regular Dirichlet forms and the stochastic quantization problem. https://arxiv.org/abs/1404.2757

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