The basic bounds for control over the infinite volume limit are given here. These tools are formally independent of dimension. We give proofs for the finite volume P(φ)2 measures of Chapter 8, but the same methods apply more generally. For example, applied to lattice fields of arbitrary dimension, the bounds of this chapter do not depend on the lattice spacing. This is in contrast to the ultraviolet bounds of Chapter 8, which depend strongly on dimension. Section 12.2, i.e. integration by parts, is similarly independent of dimension.
KeywordsCovariance Operator Schwarz Inequality Gaussian Measure Multiple Reflection Reflection Operator
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