On unified representation of state vector in quantum field theory

Abstract

Hilbert spaces having non-countable bases that correspond to a sequence of non-negative integers are considered. These bases can be identified with the points on the interval (STA0,1!) from 0 to 1 by means of a one-to-one mapping. For a point gamma in STA0,1!, a Lebesgue measure dm( gamma ) is taken, and the element of the Hilbert space corresponding to gamma is found as an integral function with respect to dm( gamma ). This integral function is a unified single integral that uses generalized distributions. (T.F.H.)