Interacting quantum fields

A wide class of quantum field theories (QFTs) describing interacting neutra l scalar bosons are constructed. It is shown that a redefinition of the vac uum expectation values (VEV) of quantum fields as generalized functions lea ds to constructions of interacting fields that are operators in a Hilbert s pace and satisfy the physical requirements for a field theory. The field op erators are constructed directly, without perturbation expansion, and const ructed in spacetime of any number of dimensions. The corresponding scatteri ng theory is developed. The limited function class underlying the QFT impos es a direction to time.