Regularized, continuum Yang-Mills process and Feynman-Kac functional integral

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Giving an ultraviolet regularization and volume cut off we construct a nuclear Riemannian structure on the Hilbert manifold $$\mathfrak{M}$$ of gauge orbits. This permits us to define a regularized Laplace-Beltrami operator δ on $$\mathfrak{M}$$ and an associated global diffusion in $$\mathfrak{M}$$ governed by δ. This enables us to define, via a Feynman-Kac integral, a Euclidean, continuum regularized Yang-Mills process corresponding to a suitable regularization (of the kinetic term) of the classical Yang-Mills Lagrangian onT $$\mathfrak{M}$$ .