Differential Calculi on the Quantum Group SUq(2)SU_q(2) and Global U(1)U(1)-covariance

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.Comment: 14 pages, late

Representation of SUq(2)SU_q(2)-covariant qq-Lie Algebra in Terms of Differential Operators

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.Comment: 11 pages, late

Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and Minimal Gauge Theory

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.Comment: 13 pages, talk at the Int. Workshop "Quantum Groups, Deformations and Contractions", Istanbul, Turkey, September, 199

Reply to the Comment by U. Jentschura and E. Weniger

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.Comment: 5 pages, revised versio

On P_T-distribution of gluon production rate in constant chromoelectric field

A complete expression for the p_T-distribution of the gluon production rate in the homogeneous chromoelectric field has been obtained. Our result contains a new additional term proportional to the singular function \delta(p_T^2). We demonstrate that the presence of this term is consistent with the dual symmetry of QCD effective action and allows to reproduce the known result for the total imaginary part of the effective action after integration over transverse momentum.Comment: 4 pages, no figures, minor corrections, one reference adde

Non-Topological Gauss-Bonnet type model of gravity with torsion

A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We demonstrate that the model admits a propagating torsion unlike the case of the topological Lovelock gravity. Due to additional symmetries of the proposed Gauss-Bonnet type Lagrangian the torsion has a reduced set of dynamical degrees of freedom corresponding to the spin two field, U(1) gauge vector field and spin zero field. A remarkable feature is that the kinetic part of the Hamiltonian containing the spin two field is positively defined. We perform one-loop quantization of the model for a special case of constant Riemann curvature space-time background treating the torsion as a quantum field variable. We discuss a possible mechanism of emergent Einstein gravity as an effective theory which can be induced due to quantum dynamics of torsion.Comment: 9 pages, no figures, minor corrections, text improve

Lorentz Gauge Gravity and Induced Effective Theories

We develop the gauge approach based on the Lorentz group to the gravity with torsion. With a Lagrangian quadratic in curvature we show that the Einstein-Hilbert action can be induced from a simple gauge model due to quantum corrections of torsion via formation of a gravito-magnetic condensate. An effective theory of cosmic knots at Planckian scale is proposed.Comment: 6 pages, talk given at International Workshop "Supersymmetries and Quantum Symmetries", JINR, Dubna, Russia, July 27-31, 200

Torsion as a dynamic degree of freedom of quantum gravity

The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A_{\mu cd} is developed. We consider SO(1,3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum gravity. The torsion is proposed to represent a dynamic degree of freedom of quantum gravity at scales above the Planckian energy. The Einstein-Hilbert theory is induced as an effective theory due to quantum corrections of torsion via generating a stable gravito-magnetic condensate. We conjecture that torsion possesses an intrinsic quantum nature and can be confined. A minimal Abelian projection for the Lorentz gauge model has been constructed, and an effective theory of the cosmic knot at the Planckian scale is proposed.Comment: 13 pages, reduced final versio

A Stable Magnetic Background in SU(2) QCD

Motivated by the instability of the Savvidy-Nielsen-Olesen (SNO) vacuum we make a systematic search for a stable magnetic background in pure SU(2) QCD. It is shown that Wu-Yang monopole-antimonopole pair is unstable under vacuum fluctuations. However, it is shown that a pair of axially symmetric monopole-antimonopole string configuration is stable, provided the distance between the two strings is small enough (less than a critical value). The existence of a stable monopole-antimonopole string background strongly supports that a magnetic condensation of monopole-antimonopole pairs can indeed generate a dynamical symmetry breaking, and thus a desired magnetic confinement of color, in QCD

Magnetic Confinement in QCD

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.Comment: 4 pages, no figure, PRL format. submitted to Phys. Lett.