Gauge parameter dependence in gauge theories (revised: subsection 2.3)

Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation.Comment: 6, MPI-PhT/94-34, BUTP-94/1

Further comments on the background field method and gauge invariant effective actions

The aim of this paper is to give a firm and clear proof of the existence in the background field framework of a gauge invariant effective action for any gauge theory ({\it background gauge equivalence}). Here by effective action we mean a functional whose Legendre transform restricted to the physical shell generates the matrix elements of the connected $S$-matrix. We resume and clarify a former argument due to Abbott, Grisaru and Schaefer based on the gauge-artifact nature of the background fields and on the identification of the gauge invariant effective action with the generator of the proper, background field, vertices.Comment: 21 pages, Latex 2

A nilpotent symmetry of quantum gauge theories

For the Becchi-Rouet-Stora-Tyutin (BRST) invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher order ghost terms are also possible.Comment: RevTeX, 9 pages, several changes to include generalizations to quartic and higher ghost terms and non-linear gauges. Abstract changed. Final version to be publishe

Axial anomalies in gauge theory by exact renormalization group method

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff \L and the boundary conditions for the relevant couplings. The physical theory is obtained at \L=0. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point \L=\L_0\to\infty but at the physical value \L=0. As an illustration, we compute the triangle axial anomalies.Comment: 11 pages + 1 appended EPS figure, LaTeX, UPRF 94-39

Gauge dependence in topological gauge theories

We parametrize the gauge-fixing freedom in choosing the Lagrangian of a topological gauge theory. We compute the gauge-fixing dependence of correlators of equivariant operators when the compactified moduli space has a non-empty boundary and verify that only a subset of these has a gauge independent meaning. We analyze in detail a simple example of such anomalous topological theories, 4D topological Yang-Mills on the four-sphere and instanton number k=1.Comment: 12 pages, TeX , harvma