The extended loop group: An infinite dimensional manifold associated with the loop space |
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Authors: | Cayetano Di Bartolo Rodolfo Gambini Jorge Griego |
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Institution: | (1) Departamento de Física, Universidad Simón Bolívar, Apartado 89000, 1080-A Caracas, Venezuela;(2) Facultad de Ciencias, Instituto de Física, Tristán Narvaja 1674, Montevideo, Uruguay |
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Abstract: | A set of coordinates in the non-parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analyzed in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered. |
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