ABSTRACT
The aim of this paper is to present a new nonstandard description of Euclidean quantum field theory as well as some of its applications. For a general discussion of nonstandard approaches to physics, see e.g.[A] and [AFHL]. In order to understand, at least at some intuitive level, the meaning of the heuristic expressions defining Euclidean quantum field measures from the physical point of view, let us begin with the simple and familiar case of Wiener measure. Let C 0[0,1] = {x ∈ C[0,1]: x(0) = 0}. C 0[0,1] endowed with the sup norm is a Banach space. Let ℬ ( C 0 [ 0 , 1 ] ) https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780367811631/7876cf56-2aaa-47b0-892b-62310007e556/content/inq_chapter16_198_1.tif"/> be the Borel σ-algebra of C 0[0,1], then Wiener measure W is defined starting from the formula
