The Small Field Parabolic Flow for Bosonic Many-body Models: Part 1 - Main Results and Algebra

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we state the main result of this analysis, outline the strategy of the proof, which uses a renormalization group flow, and perform the first, algebraic, part of a renormalization group step.