Generalized field quantization and statistics of elementary particles

Generalized schemes for the quantization of free fields based on the deformed trilinear relations of Green are investigated. A theorem shows that in reality continuous deformation is impossible. In particular, it is shown that a small violation of the ordinary Fermi and Bose statistics is impossible both in the framework of local field theory, corresponding to parastatistics of finite orders, and in the framework of nonlocal field theory, corresponding to infinite statistics. The existence of antiparticles plays a decisive role in establishing the matter case.