Geometry and Topology of Anti-BRST Symmetry in Quantized Yang-Mills Gauge Theories

TL;DR

This paper explores the geometric and topological structures of anti-BRST symmetry in quantized Yang-Mills theories, introducing new invariants and analyzing the cohomological aspects of the symmetry.

Contribution

It provides a comprehensive geometric formulation of anti-BRST symmetry, introduces Nakanishi-Lautrup invariants, and studies their topological and cohomological properties.

Findings

Defined Nakanishi-Lautrup field as a geometric object

Introduced two new topological invariants of Yang-Mills theories

Derived the anti-BRST topological index

Abstract

The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi-Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev-Popov quantization approach, the antiBRST invariance reflects thoroughly the classical symmetry of the Yang-Mills theories with respect to gauge fixing methods. The Nakanishi-Lautrup field is also defined and worked out as a geometric object. This formulation helps us to introduce two absolutely new topological invariants of quantized Yang-Mills theories, so called the Nakanishi-Lautrup invariants. The cohomological structure of the anti-BRST symmetry is also studied and the anti-BRST topological index is derived accordingly.