Proper-Time Relativistic Dynamics on Hyperboloid

Abstract

The dynamics of a point-like relativistic particle with respect of the proper time is formulated on the hyperboloid p20−p2=M2c2. The Hamilton-Jacobi equations on the hyperboloid are derived for the particles with mass (M2=m2, m>0), for the particles with zero-mass (M=0, m>0), and for the neutrino. It is shown, in a certain factorization of the momentum, the model can be identified with Nambu's three-dimensional phase space formalism. A first quantized version of the model is formulated according to a canonical scheme of quantization (Schrodinger quantization scheme).