Notes on Collective Field Theory of Large N Vector Models as Classical Mechanics on the Siegel Disc

TL;DR

This paper employs deformation quantization to formulate large N vector models as classical systems on the Siegel disc, connecting collective field theory with symplectic cocycles.

Contribution

It introduces a novel approach linking large N vector models to classical mechanics on the Siegel disc via deformation quantization.

Findings

Large N limits described as classical systems on the Siegel disc

Connection established between collective potential and symplectic cocycle

Framework bridges collective field theory and symplectic geometry

Abstract

We use deformation quantization to construct the large N limits of Bosonic vector models as classical dynamical systems on the Siegel disc and study the relation of this formulation to standard results of collective field theory. Special emphasis is paid to relating the collective potential of the large N theory to a particular cocycle of the symplectic group.