Pseudoclassical theories of majorana, weyl, and majorana-weyl particles

Pseudoclassical theories of Majorana, Weyl, and Majorana-Weyl particles in even-dimensional space-time are constructed. The canonical quantization of these theories is carried out and, as a result, the quantum-mechanical description of a neutral particle in the dimension D=2n, of a Weyl particle in D=2n, and of a neutral Weyl particle in D=4n+2 are obtained. In space-time dimensions D=2 or4 (mod 8), the description of a neutral particle coincides with the field theory description of a Majorana particle in the Foldy-Wouthuysen representation. In D=8 k+2 dimensions, the description of a neutral Weyl particle coincides with the description of a Majorana-Weyl particle.