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Communications in Mathematical Physics

, Volume 158, Issue 2, pp 217–240 | Cite as

The extended loop group: An infinite dimensional manifold associated with the loop space

  • Cayetano Di Bartolo
  • Rodolfo Gambini
  • Jorge Griego
Article

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.

Keywords

Neural Network Manifold Nonlinear Dynamics Quantum Gravity Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Cayetano Di Bartolo
    • 1
  • Rodolfo Gambini
    • 2
  • Jorge Griego
    • 2
  1. 1.Departamento de FísicaUniversidad Simón BolívarCaracasVenezuela
  2. 2.Facultad de CienciasInstituto de FísicaMontevideoUruguay

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