Narrow Results

The gauge dependence problem existing in the original Gribov–Zwanziger theory is discussed.

The gauge dependence problem of the effective action for general gauge theories in the framework of a modified functional renormalization group approach proposed recently is studied. It is shown that the effective action remains gauge-dependent on-shell.

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed.

We study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant gauges where the Wilsonian infrared cutoff Λ is inserted as a mass term for the propagating fields. In this way the Ward–Takahashi identities are preserved to all scales. Nevertheless BRST-invariance in broken and the theory is gauge-dependent and unphysical at Λ≠0. Then we discuss the infrared limit Λ→0. We show that the singularities of the axial gauge choice are avoided in planar gauge and light-cone gauge. In addition the issue of on-shell divergences is addressed in some explicit example. Finally the rectangular Wilson loop of size 2L×2T is evaluated at lowest order in perturbation theory and a noncommutativity between the limits Λ→0 and T→∞ is pointed out.

We consider first-order transition amplitudes in external fields in QED in the expanding de Sitter space and point out that they are gauge dependent quantities. We examine the gauge variations of the amplitudes assuming a decoupling of the interaction at large times, which allows to conclude that the source of the problem lies in the fact that the frequencies of the modes in the infinite future become independent of the comoving momenta. We show that a possibility to assure the gauge invariance of the external field amplitudes is to restrict to potentials which vanish sufficiently fast at infinite times, and briefly discuss a number of options in the face of the possible gauge invariance violation in the full interacting theory.