Pseudoclassical theories of Majorana, Weyl, and Majorana–Weyl particles

Pseudoclassical theories of Majorana, Weyl and Majorana–Weyl particles in even-dimensional space-times are constructed. The canonical quantization of these theories is carried out and as a result the quantum mechanical description of neutral particle in $D=2n$, Weyl particle in $D=2n$ and neutral Weyl particle in $D=4n+2$ is obtained. In $D=2,4\pmod8$ dimensional space-time the description of the neutral particle coincides with the field theoretical description of the Majorana particle in the Foldy–Wouthuysen representation. In $D=8k+2$ dimensions the description of neutral Weyl particle coincides with the description of Majorana–Weyl particle.