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Electromagnetic and gravitational interactions of the spinning particle. (English) Zbl 1112.83007
Summary: We consider the invariance of the spinning free particle Lagrangian under the global coordinate transformations for the classical model of the electron with internal degrees of freedom and obtain the conservation of the energy-momentum, total angular momentum, and electric charge. The local gauge transformations give the electromagnetic and gravitational interactions of the spinning particle in the Riemann-Cartan space from the generalized spin connections. We show that the covariant constancy of the Dirac matrices gives; (i) the form invariance of the classical equations of motion, except the gravitational force terms in nongeodesic equation, (ii) the conservation of the electromagnetic current, (iii) the quantum Hamiltonian and equations of motion from the classical ones without the quantum ordering corrections, and (iv) the minimal coupling of the gravitation with the spinning particle in the Hamiltonian and in wave equations in the Riemann-Cartan space-time.
##### MSC:
 83Cxx General relativity