Computer Science
Scientific paper
Apr 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988gregr..20..371c&link_type=abstract
General Relativity and Gravitation, Volume 20, Issue 4, pp.371-382
Computer Science
8
Field Theories:Gravitation Theory, Gravitation Theory:Field Theories
Scientific paper
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.
Chisholm S. R. J.
Farwell R. S.
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