论文标题
3D中阳米尔斯的随机定量
Stochastic quantisation of Yang-Mills-Higgs in 3D
论文作者
论文摘要
我们定义了与Yang-Mills-Higgs（YMH）理论的随机定量方程相关的状态空间和Markov过程。状态空间$ \ MATHCAL {s} $是分布的非线性度量空间，其元素可以用作具有良好连续性属性的（确定性和随机）YMH流的初始条件。使用确定性YMH流的量规协方差，我们将规范等价$ \ sim $扩展到$ \ Mathcal {s} $，从而定义了“ Gauge Orbits” $ \ Mathfrak {O} $的商空间。我们使用规律性结构理论来证明对重量化随机YMH流动的时间解决方案。此外，通过利用较小的噪声限制的对称性论点，我们表明有独特的重态化反应选择，使得这些解决方案在法律上是协方差的。这使我们能够在$ \ mathfrak {o} $（最多可与随机YMH流相关的潜在有限时间爆炸）上定义一个规范的马尔可夫进程。
We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (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 blow-up) associated to the stochastic YMH flow.
