2006/11/30 by Marat C. Reyes
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1063/1.2716991
published as J.Math.Phys.48:052301,2007 · 15 pages,2 figures, section 5, typos; To be published in J. Math. Phys. vol.48, 2007
arxiv created 2007/03/02 · openalex publication_date 2007/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.