Yang-Mills for probabilists. (English) Zbl 1430.81054
Friz, Peter (ed.) et al., Probability and analysis in interacting physical systems. In honor of S. R. S. Varadhan. Based on a workshop on the occasion of Varadhan’s 75th birthday, TU Berlin, Germany, August 15–19, 2016. Cham: Springer. Springer Proc. Math. Stat. 283, 1-16 (2019).
Summary: The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This article presents a formulation of some of the core aspects this problem as problems in probability theory. The presentation begins with an introduction to the basic setup of Euclidean Yang-Mills theories and lattice gauge theories. This is followed by a discussion of what is meant by a continuum limit of lattice gauge theories from the point of view of theoretical physicists. Some of the main issues are then posed as problems in probability. The article ends with a brief review of the mathematical literature.
For the entire collection see [Zbl 1423.60006].
For the entire collection see [Zbl 1423.60006].
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 81T25 | Quantum field theory on lattices |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
