Student Probability Seminar

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Quantum Field Theories and Probability

Speaker: Omar Abdelghani, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 31, 2025, 11 a.m.

Synopsis:

Quantum field theories are the most successful models of fundamental physics in history. Yet a complete understanding of their mathematical structure is a longstanding open problem in 3+1 dimensions. However, after a flurry of work in the 70s, we have a beautiful axiomatic theory for these objects that combines functional analysis, Fourier analysis, representation theory, and the theory of distributions. In this talk, I will give an overview of some of these ideas (codified in the Wightman axioms), the interpretation of quantum theories as generalized probability theories, and the duality between quantum field theories and the Euclidean-invariant random fields that have recently enjoyed a resurgence in popularity among probabilists. If time permits, I will also briefly discuss how probabilistic methods have been used to construct quantum fields in 1 + 1D  and 2 + 1D.