Propertime theories and reparametrization-invariant theories

Abstract

Reparametrization-invariant theories of point relativistic particle interaction with fields of arbitrary tensor dimension are considered. It has been shown that the equations of motion obtained by Kalman [G. Kalman, Phys. Rev. vol.123, p.384 (1961)] are reproduced as the Euler - Lagrange equations for reparametrization-invariant theory in the propertime gauge. The formalism is developed that conserves manifest reparametrization invariance at each stage of calculations. Using the above formalism, the equations of motion are being analyzed and the dynamical variable theories are being constructed. It has been shown that the remained invariance kept after gauge fixation gives an identically-zero invariant Hamiltonian.