On the model of the relativistic particle with curvature and torsion

Abstract

Two integrals along the world trajectory of its curvature and torsion are added to the standard action for the point-like spinless relativistic particle. Since here the three-dimensional space-time is considered at the beginning, the torsion of the world curve is defined with a sign in contrast to the previous consideration: V. V. Nesterenko, J. Math. Phys. 32, 3315 (1991). Upon obtaining a complete set of constraints in the phase space a generalized Hamiltonian description of a new version of the model is constructed. This enables one to quantize the model canonically and to derive exactly the relation between the spin and mass of the states.