On a Possibility of a Further Generalization of Field Quantization

Abstract

A possibility is suggested of a further generalization of the method of field quantization which was developed in our previous paper. Only the R-method is considered in this paper. The generalization consists in modifying the expression for the number operators in terms of creation and annihilation operators, which is analogous to the expression for the spin operator in the general theory of relativistic wave equations of Dirac-Pauli-Fierz and Harish-Chandra. Such a generalization leads to new results only in the cases of order (s - 1) ⩾3. Quantum mechanics of a simple harmonic oscillator is discussed in detail, and generalized commutation relations are given. Field theory quantized by our method is studied and some general features are discussed. It is shown that in the cases of (s - 1) ⩾3 the field theory thus obtained is in general not equivalent to ordinary para-field theory.