Stochastic quantization, large N, and mean field limit

Abstract: We study "large N problems” in quantum field theory using SPDE methods via stochastic quantization. In the SPDE setting this is formulated as mean field problems. We will consider the vector Phi^4 model (i.e. linear sigma model), whose stochastic quantization is a system of N coupled dynamical Phi^4 SPDEs. We discuss a series of results. First, in 2D, we prove mean field limit for these dynamics as N goes to infinity. We also show that the quantum field theory converges to massive Gaussian free field in this limit, in both 2D and 3D. Moreover we prove exact formulae for some correlations of O(N)-invariant observables in the large N limit; such formulae were predicted using “bubble diagrams” in physics.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

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