Canonical Formalism and Equations of Motion for a Spinning Particle in General Relativity

摘要

A canonical formalism for spinning particles suitable for the formulation of a general relativistic covariant statistical mechanics of particles endowed with spin has been developed. For that purpose the bracket for internal and external variables has been given. In particular, limiting ourselves to the spin tensor S/sup mu nu / it has been possible to define momenta which are the true conjugates to the position variables. For the case considered the Hamiltonian function in addition to the invariant ''mass'' involves only one additional scalar. The equations of motion are then found by calculating the brackets of the dynamical variables with that Hamiltonian, and are compared to those obtained by other methods. The conjugate variables in the internal space which has to be adjoined to the (eight-dimensional) phase space for a complete covariant description of spinning particles have also been given. (author). 22 refs. (Atomindex citation 19:060025)