Geometry and topology of anti-BRST symmetry in quantized Yang–Mills gauge theories

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