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On the non-relativistic limit of a spin-12 particle in a classical gravitational field

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  • Bäuerle, G.G.A.
  • Twelker, H.F.

Abstract

An external gravitational field modifies the description of a spin-12 particle in various ways. For instance, the inner product of Dirac wave functions, and the equal-time anti-commutation relations and the canonical energy-momentum tensor of the quantized Dirac field are modified. This has the following consequences. The Dirac-Hamiltonian (2.29) of a spin-12 particle in a time-dependent gravitational field is not Hermitian. Furthermore, the Euler-Lagrange equation and the Heisenberg equation for the quantized Dirac field are not consistent. We obviate these deficiencies by the introduction of the η-field as the fundamental variable instead of the Dirac field. At the same time, the non-relativistic limit is most conveniently discussed in the η-description. For this purpose, we introduce a modification of the Foldy-Wouthuysen transformation.

Suggested Citation

  • Bäuerle, G.G.A. & Twelker, H.F., 1985. "On the non-relativistic limit of a spin-12 particle in a classical gravitational field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(3), pages 553-564.
    • Handle: RePEc:eee:phsmap:v:130:y:1985:i:3:p:553-564
    DOI: 10.1016/0378-4371(85)90045-7
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    Cited by:

    1. Kraeft, W.D. & Strege, B., 1988. "Energy loss of charged particles moving in a plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(1), pages 313-322.

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