Kaluza-Klein approach to the motion of non-Abelian charged particles with spin
- 1 August 1991
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 8 (8) , 1427-1444
- https://doi.org/10.1088/0264-9381/8/8/009
Abstract
The equations of motion for charged spinning particles in a background of gravitational and Yang-Mills fields are derived within the Kaluza-Klein framework, using Grassmannian variables to describe spin. Both the Lagrangian and Hamiltonian frameworks are used, the geometry being interpreted in a supermanifold setting. It is found that a gauge supersymmetric coupling leads to the most natural equations of motion, after reduction by the odd supersymmetry transformations. This requires a modification of the Lagrangian, obtained by replacing the Levi-Civita connection over the Yang-Mills bundle by one with torsion given by the Chern-Simons 3-form.Keywords
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