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Einstein - Cartan - Dirac theory in the low-energy limit

P Singh et al 1997 Class. Quantum Grav. 14 3513-3525   doi: 10.1088/0264-9381/14/12/031  Help

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P Singh and L H Ryder
Physics Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NR, UK

Abstract. We look for manifestations of the effects of torsion in the low-energy limit in the context of Einstein - Cartan - Dirac theory (or any theory of gravity in which the torsion tensor is purely axial). To proceed, we introduce the mathematical law governing the transport of orthonormal bases or tetrads in a spacetime with torsion. This law is applied to compute the metric and connection in a rotating and accelerating frame, or laboratory. A spin- particle is placed in this rotating and accelerating frame and the low-energy limit of the Dirac equation is taken by means of the Foldy - Wouthuysen transformation. In addition to obtaining the Bonse - Wroblewski phase shift due to acceleration, Sagnac-type effects, rotation - spin couplings of the Mashhoon type, redshift of the kinetic energy and the spin - orbit coupling term of Hehl and Ni, we also obtain several interesting and significant terms as a consequence of introducing torsion into spacetime. We give a detailed interpretation of these additional terms and discuss their observability in the light of current well-known experimental techniques.

PACS numbers: 0450, 0480, 9530S

Print publication: Issue 12 (December 1997)
Received 2 June 1997, in final form 24 September 1997

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