An infinite-dimensional calculus for gauge theories

  title={An infinite-dimensional calculus for gauge theories},
  author={Rui Vilela Mendes},
  • R. Mendes
  • Published 8 May 2010
  • Physics, Mathematics
IPFN EURATOM/IST Association, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal, CMAF, Complexo Interdisciplinar, Universidade de Lisboa, Av. Gama Pinto, 2 1649-003 Lisboa (Portugal), e-mail: 

Figures from this paper

Stochastic evolution equations with Wick-polynomial nonlinearities

We study nonlinear parabolic stochastic partial differential equations with Wickpower and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the


We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic



Stratification of the orbit space in gauge theories: the role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for

Representations of the holonomy algebras of gravity and nonAbelian gauge theories

Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a

Projective techniques and functional integration for gauge theories

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then

Asymptotic dynamics for gauge theories

Rigorous methods are used to analyze the asymptotic (large time) behavior of gauge-theory Hamiltonians in the interaction picture. A simple ''asymptotic dynamics'' for four-dimensional gauge theories

Hyphs and the Ashtekar–Lewandowski measure

Differential geometry on the space of connections via graphs and projective limits

Stratification of the Generalized Gauge Orbit Space

Abstract: Different versions for defining Ashtekar's generalized connections are investigated depending on the chosen smoothness category for the paths and graphs – the label set for the projective

Stochastic processes and the non-perturbative structure of the QCD vacuum

Based on a local Gaussian evaluation of the functional integral representation, a method is developed to obtain ground state functionals. The method is applied to the gluon sector of QCD. For the

On the support of the Ashtekar-Lewandowski measure

AbstractWe show that the Ashtekar-Isham extension $$\overline {A/G}$$ of the configuration space of Yang-Mills theories $$A/G$$ is (topologically and measure-theoretically) the projective limit of

On Gell-Mann's ~.-Matrices, d- and j:Tensors, Octets, and Parametrizations of S U(3)

The algebra of SU(3) is developed on the basis of the matrices 2~ of GE~L-MAN~-, and identities involving the tensors d~j~ and f~#~ oceurr'mg in their multiplication law are derived. Octets and the