THE DIRAC-EQUATION IN THE ROBERTSON-WALKER SPACE-TIME

The Dirac equation is considered, via the Newman-Penrose formalism, in the context of the Robertson-Walker geometry. The solution of the equ ation, which contrary to the neutrino case is not directly separable, is reduced to the study of decoupled spatial and temporal equations. T he spatial equations are explicitly integrated and show the existence of discrete energy levels in case of closed universe. Besides the neut rino, the time equation is discussed in limiting situations of the sta ndard cosmology. (C) 1996 American Institute of Physics.