Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-15
J.Math.Phys.48:052301,2007
Physics
High Energy Physics
High Energy Physics - Theory
15 pages,2 figures, section 5, typos; To be published in J. Math. Phys. vol.48, 2007
Scientific paper
10.1063/1.2716991
A set of differential operators acting by continuous deformations on path dependent functionals of open and closed curves is introduced. Geometrically, these path operators are interpreted as infinitesimal generators of curves in the base manifold of the gauge theory. They furnish a representation with the action of the group of loops having a fundamental role. We show that the path derivative, which is covariant by construction, satisfies the Ricci and Bianchi identities. Also, we provide a geometrical derivation of covariant Taylor expansions based on particular deformations of open curves. The formalism includes, as special cases, other path dependent operators such as end point derivatives and area derivatives.
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