Dimensional reduction and gauge group reduction in Bianchi-type cosmology

J. M. Pons and L. C. Shepley
Phys. Rev. D 58, 024001 – Published 5 June 1998
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Abstract

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.

  • Received 6 February 1998

DOI:https://doi.org/10.1103/PhysRevD.58.024001

©1998 American Physical Society

Authors & Affiliations

J. M. Pons*

  • Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, and Institut de Física d’Altes Energies, Diagonal 647, E-08028 Barcelona, Catalonia, Spain

L. C. Shepley

  • Center for Relativity, Physics Department, The University of Texas, Austin, Texas 78712-1081

  • *Electronic address: pons@ecm.ub.es
  • Electronic address: larry@helmholtz.ph.utexas.edu

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Vol. 58, Iss. 2 — 15 July 1998

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