Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

Details Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

2005-05-04

arxiv.org/abs/gr-qc/0505021v2

Class.Quant.Grav. 22 (2005) 3203-3222

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages

Scientific paper

10.1088/0264-9381/22/16/006

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.

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