University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A PDE construction of the Euclidean $\Phi^4_3$ quantum field theory

A PDE construction of the Euclidean $\Phi^4_3$ quantum field theory

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact INI IT.

SRQW02 - Quantum field theory, renormalisation and stochastic partial differential equations

We present a self-contained construction of the Euclidean $Phi4$ quantum field theory on $mathbb{R}3$ based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on $mathbb{R}^3$ defined on a periodic lattice of mesh size $varepsilon$ and side length $M$. We introduce an energy method and prove tightness of the corresponding Gibbs measures as $varepsilon ightarrow 0$, $M ightarrow infty$. We show that every limit point satisfies reflection positivity, translation invariance and nontriviality (i.e. non-Gaussianity). Our argument applies to arbitrary positive coupling constant and also to multicomponent models with $O(N)$ symmetry. Joint work with Massimiliano Gubinelli.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity