Operator realization of generalized Pauli-Villars regularization

Vector space of “quasistates” is constructed, in which the notion of “field operator at fixed point” can be determined. The usual and chronological products of “fields at fixed point” are defined as operators in this space. In the space of quasistates there is a subspace of “regular quasistates”, which can be provided with a norm and scalar product. When the factorisation over this norm is performed, the space of regular quasistates acquires the structure of the usual Fock space of states. Reduction of operators corresponding to the usual and chronological products of the fields, from the space of quasistates to the subspace of regular quasistates generates operator-valued distributions in the Fock space. Thus the regularisation procedure turns out to be incorporated intrinsically in the construction of the vector space.