Quantization of massive Weyl fields in vacuum

We briefly review the main methods for the description of massive Weyl fields in vacuum. On the classical level we discuss Weyl fields expressed through Grassmann variables as well as having spinors with commuting components. In both approaches we quantize the system. We get the correct anticommutation relations between creation and annihilation operators, which result in the proper form of the total energy of the field. However, the commuting classical Weyl fields require the new method of quantization.