General Relativity and Gravitation

, Volume 9, Issue 7, pp 621–635 | Cite as

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

  • N. C. T. Coote
  • A. J. Macfarlane
Research Articles

Abstract

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient ω aμb , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative ofψ is built with the aid of the vierbein instead of with ω aμb . This still yields a first-order formalism, but one in which ω aμb is related to the vierbein in the same way as it would be in the absence ofψ. This ensures that the global connection Г μν α remains symmetric inμ andv in the presence ofψ. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.

Keywords

Field Equation Classical Theory Gravitational Field Einstein Equation Spinor Field 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • N. C. T. Coote
    • 1
  • A. J. Macfarlane
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeEngland

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