Chen Integrals, Generalized Loops and Loop Calculus

• Type: Article in International Scientific Journal
• Date: 1994

Authors

João Tavares (Author) FCUP

Journal

Title: International Journal of Modern Physics A

Vol. 9 No. 26

Pages: 4511-4548

ISSN: 0217-751X

Publisher: World Scientific

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Abstract (EN): We use Chen iterated line integrals to construct a topological algebra Ap of separating functions on the Group of Loops LMp. Ap has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops L]Mp. Then we develope a Loop Calculus, based on the Endpoint and Area Derivative Operators, providing a rigorous mathematical treatment of early heuristic ideas of Gambini, Trias and also Mandelstam, Makeenko and Migdal. Finally we define a natural action of the ”pointed” diffeomorphism group Diffp(M) on L]Mp, and consider a Variational Derivative which allows the construction of homotopy invariants. This formalism is useful to construct a mathematical theory of Loop Representation of Gauge Theories and Quantum Gravity.

Language: English

Type (Professor's evaluation): Scientific