Stochastic quantisation of YangMillsHiggs in 3D
Abstract
We define a state space and a Markov process associated to the stochastic quantisation equation of YangMillsHiggs (YMH) theories. The state space $\mathcal{S}$ is a nonlinear metric space of distributions, elements of which can be used as initial conditions for the (deterministic and stochastic) YMH flow with good continuity properties. Using gauge covariance of the deterministic YMH flow, we extend gauge equivalence $\sim$ to $\mathcal{S}$ and thus define a quotient space of "gauge orbits" $\mathfrak{O}$. We use the theory of regularity structures to prove local in time solutions to the renormalised stochastic YMH flow. Moreover, by leveraging symmetry arguments in the small noise limit, we show that there is a unique choice of renormalisation counterterms such that these solutions are gauge covariant in law. This allows us to define a canonical Markov process on $\mathfrak{O}$ (up to a potential finite time blowup) associated to the stochastic YMH flow.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.03487
 Bibcode:
 2022arXiv220103487C
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 151 pages