Low-energy general relativity with torsion: A systematic derivative expansion

Dmitri Diakonov, Alexander G. Tumanov, and Alexey A. Vladimirov
Phys. Rev. D 84, 124042 – Published 19 December 2011

Abstract

We attempt to build systematically the low-energy effective Lagrangian for the Einstein-Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order, the fermion action with torsion possesses additional U(1)L×U(1)R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a pointlike 4-fermion action of a general form containing vector-vector, axial-vector, and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the “spin fluid” approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.

  • Figure
  • Received 17 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.124042

© 2011 American Physical Society

Authors & Affiliations

Dmitri Diakonov1,2, Alexander G. Tumanov2, and Alexey A. Vladimirov3

  • 1Petersburg Nuclear Physics Institute, Gatchina 188300, St. Petersburg, Russia
  • 2St. Petersburg Academic University, St. Petersburg 194021, Russia
  • 3Ruhr-Universität Bochum, Bochum D-44780, Germany

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Issue

Vol. 84, Iss. 12 — 15 December 2011

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