Normalization invariance in quantum field theories

Starting with a lattice formulation of the Feynman-Kac functional integrals defining a quantum field theory, we show that the lack of dependence of the integrals on the ''normalization'' of the bosonic fields leads to a whole class of different functional formulas for the Schwinger functions. These new formulas are all equivalent to the standard ones, but have several advantages that are elucidated. The method is applied to (phi4)/sub d/ theories, d = 1, 2, 3, 4, and scalar QED. In addition to the general definition of ''normalization invariance,'' the results in this paper include (i) a functional definition of the Borel transform in the bare coupling, (ii) manifest cut-plane analyticity of the Borel variable, as is the onset of the cut, and (iii) cut-plane analyticity of lattice g0(phi4)/sub d/ theory in g0