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General Relativity and Gravitation

, Volume 20, Issue 4, pp 371–382 | Cite as

Gravity and the frame field

  • J. S. R. Chisholm
  • R. S. Farwell
Research Articles

Abstract

The covariant derivative of a single massive fermion field on a Riemannian manifold is defined. The standard method of defining free bosonic Lagrangians from the fermion covariant derivative does not give the usual Lagrangian density for the free gravitational field. We express the fermion Lagrangian mass term as a “frame field” term added to the covariant derivative; this “extended covariant derivative” defines a gravitational Lagrangian density proportional to the usual scalar curvatureR, plus a term quadratic in the curvature components. The quadratic term is expected to be negligible at distances much greater than the fermion Compton wavelength, and is of a general form widely studied in recent years. The frame field term used to derive this gravitational Lagrangian is essentially the same as that used previously to derive the electroweak interaction boson mass matrix without using the Higgs-Kibble mechanism.

Keywords

Manifold Riemannian Manifold Scalar curvatureR Covariant Derivative Boson Mass 
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

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • J. S. R. Chisholm
    • 1
  • R. S. Farwell
    • 2
  1. 1.University of KentCanterburyEngland
  2. 2.St. Mary's CollegeTwickenhamEngland

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