# Construction of (λɸ^{4}-σɸ^{2}-μɸ)_{3} Quantum Field Models

## Abstract

This lecture is intended to introduce the audience to some constructions of theories for the boson field models in three dimensional space-time, which exhibit ultraviolet divergences. Constructive quantum field theory has developed rapidly in the past few years. The polynomial interactions in two dimensional space-time (the P (ɸ)_{2} models) are the best behaved models and its detailed structure is now well-known [2, 12, 16, 18, 19, 23, 24, 28, 30, 36, 37, 40]. Most of you may have already been exposed in the construction of the P(ɸ)_{2} model elsewhere (at least, you will have a change again in Prof. Challifour’s lecture at this school) and so I will not 42 discuss that subject. The (λɸ^{4}-σɸ^{2}-μɸ) interactions in three dimensional space-time (the (λɸ^{4}-σɸ^{2}-μɸ)_{3} models), which we are considering here, are the next well behaved, models. These differ from P(ɸ)_{2} by having ultraviolet divergences and by requiring ultraviolet mass wave functions as well as vacuum energy renormalizations [14, 15].

## Keywords

Field Model Lattice Approximation Cluster Expansion Uniform Bound Ultraviolet Divergence## Preview

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