Continuum regularization of quantum field theory: (I). Scalar prototype

This paper, I, is the first in a series of papers in which we present a new, presumably nonperturbative, regularization scheme for continuum quantum field theory. The higher covariant derivative method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. We will discuss gauge theories explicitly in II. This first paper on scalar field theory is designed partly as a pedagogical vehicle to introduce the reader, in the simplest possible context, to the relevant regularized Langevin and regularized Schwinger-Dyson techniques — which extend more or less directly to gauge theory. The scalar context is also the simplest in which to study the curious feature that our scheme is not an action regularization, a fact which is crucial to its success in regulating theories with local symmetries. A renormalization program is checked through one loop, including a computation of the β-function in φ 6 3.