Two--Dimensional BF Model Quantized in the Axial Gauge

TL;DR

This paper quantizes the 2D topological BF model in the axial gauge, demonstrating its ultraviolet finiteness and addressing the infrared issues unique to this gauge, while highlighting differences from the 3D case.

Contribution

It provides a detailed quantization of the 2D BF model in the axial gauge, revealing its finiteness and the necessity of equations of motion alongside Ward identities.

Findings

The model is trivially ultraviolet finite.

Infrared problems are replaced by a solvable long-distance issue.

The action principle cannot be fully replaced by Ward identities.

Abstract

The two--dimensional topological BF model is quantized in the axial gauge. We show that this theory is trivially ultraviolet finite and that the usual infrared problem of the propagator of the scalar field in two dimensions is replaced by an easily solvable long distances problem inherent to the axial gauge. It will also be shown that contrarily to the 3--dimensional case, the action principle cannot be completely replaced by the various Ward identities expressing the symmetries of the model; some of the equation of motion are needed.