arXiv subjects
Publications and source records attributed to D. G. Pak.
It is shown that the criticism (revised version) made in hep-th/0007108 (by Jentschura and Weniger) on hep-th/0006057 has no valid ground. Furthemore we emphasize that the concept of the electric-magnetic duality used in the analysis of QED one-loop effective action in physics/0010038 (by Jentschura) has first been introduced in hep-th/0006057.
Recently we have obtained a non-perturbative but convergent series expression of the one loop effective action of QED, and discussed the renormalization of the effective action. In this paper we establish the electric-magnetic duality in the quantum effective action.
The one-loop effective action of QED obtained by Euler and Heisenberg and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this letter we present a non-perturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one loop effective action of QED.
We present a gauge independent method to construct the effective action of QCD, and calculate the one loop effective action of $SU(2)$ QCD in an arbitrary constant background field. Our result establishes the existence of a dynamical symmetry breaking by demonstrating that the effective potential develops a unique and stable vacuum made of the monopole condensation in one loop approximation. This provides a strong evidence for the magnetic confinement of color through the dual Meissner effect in the non-Abelian gauge theory. The result is obtained by separating the topological degrees which describe the non-Abelian monopoles from the dynamical degrees of the gauge potential, and integrating out all the dynamical degrees of QCD. We present three independent arguments to support our result.
We present a strong evidence for the magnetic confinement in QCD by demonstrating that the one loop effective action of SU(2) QCD induces a dynamical symmetry breaking thorugh the monopole condensation, which could induce the dual Meissner effect and guarantee the confinement of color in the non-Abelian gauge theory. The result is obtained by separating the topological degrees which describes the non-Abelian monopoles from the dynamical degrees of the potential, and integrating out all the dynamical degrees of QCD.
Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus on SU_q(2) is uniquely defined. A non-standard Leibnitz rule is proposed for the exterior differential. The minimal gauge theory with SU_q(2) quantum group symmetry is considered.
We derive a generalized Skyrme-Faddeev action as the effective action of QCD in the low energy limit. Our result demonstrates the existence of a mass gap in QCD which triggers the confinement of color.
A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed in terms of differential operators. A gauge covariant differential algebra is uniquely determined. The non-standard Leibnitz rule is obtained for a corresponding $q$-Lie algebra.
A three-dimensional $q$-Lie algebra of $SU_q(2)$ is realized in terms of first- and second-order differential operators. Starting from the $q$-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The proposed construction is inverse to the standard Woronowicz approach; the left-invariant vector fields are introduced as initial objects whereas the differential 1-forms are defined in a dual manner.