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SUMMARY:A PDE construction of the Euclidean $\\Phi^4_3$ quantum field theo
 ry - Martina Hofmanova (Bielefeld University)
DTSTART:20181025T130000Z
DTEND:20181025T140000Z
UID:TALK113020@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We present a self-contained construction of the Euclidean $Phi
 ^4$ quantum field theory on $mathbb{R}^3$ based on PDE arguments. More pre
 cisely\, we consider an approximation of the stochastic quantization equat
 ion on $mathbb{R}^3$ defined on a periodic lattice of mesh size $varepsilo
 n$ and side length $M$. We introduce an energy method and prove tightness 
 of the corresponding Gibbs measures as $varepsilon  ightarrow 0$\, $M  igh
 tarrow infty$. We show that every limit point satisfies reflection positiv
 ity\, translation invariance and nontriviality (i.e. non-Gaussianity). Our
  argument applies to arbitrary positive coupling constant and also to mult
 icomponent models with $O(N)$ symmetry. Joint work with Massimiliano Gubin
 elli.
LOCATION:Seminar Room 1\, Newton Institute
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