RELATIVISTIC QUANTUM MECHANICS FOR SCALAR PARTICLES AND SPINOR PARTICLES IN THE BELTRAMI-DE SITTER SPACETIME
Beltrami-de Sitter时空中标量和旋量粒子的量子理论

Following the procedure to transmute the relativistic theory of classical particles to quantum theory in the Minkowski spacetime, we have proposed a scheme to establish relativistic wave equations for scalar particles and spinor particles in the Beltrami-de Sitter spacetime. It is shown that these equations are invariant under the transformations of the de Sitter group and are just the Klein-Gordon equation and the Dirac equation in the Beltrami-de Sitter spacetime respectively. The eigenfunctions and the corresponding discrete eigenvalues of these equations on the metric of a family of space-like simultaneous hypersurfaces in the Beltrami-de Sitter spacetime have been obtained.