Regularized, continuum Yang-Mills process and Feynman-Kac functional integral
Copyright policy )Regularized, continuum Yang-Mills process and Feynman-Kac functional integral
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\(\mathfrak{M}\).
- Sorbonne Paris Cité France
- Laboratory of Theoretical and High Energy Physics France
- Sorbonne University France
volume cut-off, Diffusion processes and stochastic analysis on manifolds, Path integrals in quantum mechanics, 58D20, Feynman-Kac functional integral, constructive definition of the Yang-Mills functional path integral in the continuum, 58E17, diffussion processes in Hilbert manifolds, ultraviolet regularization, action of the group of gauge transformations on the space of generic connections, Constructive quantum field theory, Laplace-Beltrami operator, 81E10, 81C35, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Applications of manifolds of mappings to the sciences, nuclear Riemannian structures
volume cut-off, Diffusion processes and stochastic analysis on manifolds, Path integrals in quantum mechanics, 58D20, Feynman-Kac functional integral, constructive definition of the Yang-Mills functional path integral in the continuum, 58E17, diffussion processes in Hilbert manifolds, ultraviolet regularization, action of the group of gauge transformations on the space of generic connections, Constructive quantum field theory, Laplace-Beltrami operator, 81E10, 81C35, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Applications of manifolds of mappings to the sciences, nuclear Riemannian structures
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