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Stochastic quantisation of Yang-Mills
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Stochastic quantisation of Yang-Mills
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We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the stochastic quantisation equations of Yang-Mills on two and three dimensional Euclidean space with finite volume. The main result of these works is that one can renormalise the 2D and 3D stochastic Yang-Mills heat flow so that the dynamic becomes gauge covariant in law. Furthermore, there is a state space of distributional $1$-forms $\mathcal{S}$ to which gauge equivalence $\sim$ extends and such that the renormalised stochastic Yang-Mills heat flow projects to a Markov process on the quotient space of gauge orbits $\mathcal{S}/{\sim}$. In this review, we give unified statements of the main results of these works, highlight differences in the methods, and point out a number of open problems.
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Cited by 1 Pith paper
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A PDE approach to the 2D Yang-Mills measure
The 2D Yang–Mills measure on the unit square admits a Coulomb-gauge representative in every Ω^1_β, β<1 — Gaussian-free-field regularity — with L^p moments growing like p^{(2+β)/2+δ}.
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