PSEUDOCLASSICAL DESCRIPTION OF THE MASSIVE SPINNING PARTICLE IN D-DIMENSIONS

Through the dimensional reduction of the pseudoclassical Lagrangian for a massless (d + l)-dimensional spinning particle, the modified Lagrangian for a massive spin-1/2 particle in d dimensions is constructed, which turns out to be classically equivalent to the ordinary N = 1 worldline supersymmetric Lagrangian. The quantization of the modified system in d = 2n + 1 is shown to lead, unlike the ordinary pseudoclassical model, exactly to the (2n + 1)-dimensional Dirac equation, whereas in an even d = 2n the two systems are also equivalent at the quantum level and describe the states, obeying the 2n-dimensional Dirac equation.