The three-dimensional BF Model with Cosmological Term in the Axial Gauge

TL;DR

This paper quantizes the 3D BF model in axial gauge, demonstrating that Green-functions are tree graphs derived from symmetry considerations alone, without relying on an action principle.

Contribution

It shows the unique determination of the 3D BF model through symmetry, simplifying its quantization and analysis.

Findings

Green-functions correspond to tree graphs

Model can be uniquely determined by symmetry

Quantization achieved without an action principle

Abstract

We quantize the three-dimensional $BF$-model using axial gauge conditions. Exploiting the rich symmetry-structure of the model we show that the Green-functions correspond to tree graphs and can be obtained as the unique solution of the Ward-Identities. Furthermore, we will show that the theory can be uniquely determined by symmetry considerations without the need of an action principle.