Quantum Theory of Non-Local Fields. Part I. Free Fields

Abstract

The possibility of a theory of non-local fields, which is free from the restriction that field quantities are always point functions in the ordinary space, is investigated. Certain types of non-local fields, each satisfying a set of mutually compatible commutation relations, which can be obtained by extending familiar field equations for local fields in conformity with the principle of reciprocity, are considered in detail. Thus a scalar non-local field is obtained, which represents an assembly of particles with the mass, radius and spin 0, provided that the field is quantized according to the procedure similar to the method of second quantization in the usual field theory. Non-local vector and spinor fields corresponding to assemblies of particles with the finite radius and the spins 1 and $\frac{1}{2}$ respectively are obtained in the similar way.