Relativistic particle with action that depends on the torsion of the world trajectory

A generalized Hamiltonian formalism is constructed for a relativistic particle with torsion in a $D$-dimensional spacetime. The complete set of constraints is found and separated into first-and second-class constraints. The canonical quantization of the theory is treated on this basis. For $D=3$ in the sector of the theory without tachyon states, a spectral equation relating the square of the mass of a state to its spin and the parameters of the model is obtained. With increasing spin, the mass of the state decreases. Various forms of wave equation are constructed in operator form, and the particle propagator is found. The possibility of describing states with integer, half-integer, and continuous values of the spin ($D=3$) in the framework of this model is demonstrated.