Short-distance behavior of a renormalizable quantum field theory

A new method which gives the short-distance behavior of a renormalizable quantum field theory is proposed. The method does not use a lattice formulation and is based on identifying those ''paths'' which make the dominant contribution to the Feynman functional integral in a continuum theory. We apply the method to (phi4)4 theory. Our initial results show that a nontrivial ultraviolet fixed point in (phi4)4 theory must necessarily be an essential zero of the Gell-Mann--Low function, as in the case of QED. We also show that the wave-function renormalization constant Z3 does not vanish. This case is not yet included in the (phi4)4 ''triviality'' results of Froehlich and others