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

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 anti-BRST 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.