Finite anticanonical transformations in field-antifield formalism

We study the role of arbitrary (finite) anticanonical transformations in the field-antifield formalism, and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered.Comment: 31 pages, no figures, typos corrected, published versio

Representation of a gauge field via intrinsic "BRST" operator

We show that there exists a representation of a matrix valued gauge field via intrinsic "BRST" operator assigned to matrix valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang - Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.Comment: 15 pages, no figures, Section 6 extended with (6.14), (6.15); v3: Section 7 added, minor corrections; v4: Section 4, minor corrections; v5: formula (4.11) modifie

Closed description of arbitrariness in resolving quantum master equation

In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.Comment: 13 pages, v2: Section 2 extended, misprint corrected, references added, formula on page 7 corrected, new formula (4.30) and a phrase on it inserted, v3: misprints in formulas (2.12), (4.23), (4.36)-(4.39) corrected, v4: formulae (A.8), (A.11), (A.12) added, v5:published versio