The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

Details The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

1993-03-04

arxiv.org/abs/gr-qc/9303010v2

Commun.Math.Phys. 158 (1993) 217-240

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.01

Scientific paper

10.1007/BF02108073

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 analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.

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