On defining the spin moment in the tetrad theory of gravitation

Abstract

A general definition of the spin moment is presented in the tetrad formulation of the relativistic theory of gravitation; it is based on the conditions for the invariance of the corresponding action integral relative to infinitesimal tetrad transformations (the so-called tetrad spin moment) and infinitesimal coordinate transformations (the so-called coordinate spin moment). It is shown that the tetrad formulation of the general theory of relativity (TFGTR) and the tetrad theory of gravitation (TTG) in a space of absolute parallelism lead to fundamentally different definitions of spin, since in the Riemannian geometry of the TFGTR only the coordinate spin moment is physically meaningful, whereas in the space of absolute parallelism of the TTG only the tetrad spin moment has essential significance. It is also indicated that the Pellegrini-Plebanski theory (PPT) leads to an unsatisfactory hybrid definition of spin in the form of the coordinate spin moment of the gravitational and boson fields and the tetrad spin moment of the gravitational and fermion fields, the gravitational field entering into these spin moments of the PPT with opposite signs.