SPINORS IN THE DYNAMICAL THEORY OF SPINNING PARTICLES

Publisher Website
Google Scholar
Abstract
The correspondence between self-dual six-vectors and symmetric spinors of the second rank is used to put into spinor form the rotational equations of motion of a particle analogous to a pure gyroscope or to a symmetrical top. These equations are then split up into an equivalent system of equations in terms of spinors of the first rank. The Lagrangian of each system is set up, and the canonically conjugate variables obtained from it in terms of covariant spinors. But the canonical variables, being not all independent, lead to weak equations in the sense of Dirac. Therefore, Dirac's generalized Hamiltonian dynamics is used in the canonical formulation in terms of Poisson Brackets. The detailed discussion of the symmetrical top case shows that, though the fundamental Poisson Brackets for the total spin angular momentum and the "spin" are the usual ones, those Poisson Brackets-involving the derivative of the "spin" are not unique.

This publication has 3 references indexed in Scilit: