PSEUDOCLASSICAL THEORIES OF MAJORANA, WEYL, AND MAJORANA-WEYL PARTICLES

Pseudoclassical theories of Majorana, Weyl, and Majorana-Weyl particle s in even-dimensional space-time are constructed. The canonical quanti zation 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 or 4 (mod 8), the de scription of a neutral particle coincides with the field theory descri ption of a Majorana particle in the Foldy-Wouthuysen representation. I n D = 8k + 2 dimensions, the description of a neutral Weyl particle co incides with the description of a Majorane-Weyl particle.