  Most quantum field theories are not exactly solvable. In this paper show the
statistical equivalence of the standard exponential path integral to products
of Heaviside functions, i.e. a product of specially tuned uniform
distributions. This allows exact integrations of certain quantum field
theories. I apply the equivalence to calculate the exact, non-perturbative path
integral for a 3+1-D scalar (real) phi-4 field theory.
