Regularized, Continuum {Yang-Mills} Process and {Feynman-Kac} Functional Integral

Asorey, M.; Mitter, P.K.

doi:10.1007/BF01213595

Regularized, Continuum {Yang-Mills} Process and {Feynman-Kac} Functional Integral

M. Asorey
(
- Paris U., VI-VII
)
,
P.K. Mitter
(
- Paris U., VI-VII
)

Jun, 1980

24 pages

Published in:

Commun.Math.Phys. 80 (1981) 43

DOI:

10.1007/BF01213595

Report number:

PAR LPTHE 80/22

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Abstract: (Springer)

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}

.

GAUGE FIELD THEORY: YANG-MILLS
RENORMALIZATION: REGULARIZATION
FUNCTIONAL ANALYSIS
FIELD THEORY: OPERATOR ALGEBRA

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