5,244 research outputs found
Differential Calculi on the Quantum Group and Global -covariance
A variety of three-dimensional left-covariant differential calculi on the
quantum group is considered using an approach based on global -covariance. Explicit representations of possible -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 -Lie algebra.Comment: 14 pages, late
Representation of -covariant -Lie Algebra in Terms of Differential Operators
A three-dimensional -Lie algebra of is realized in terms of
first- and second-order differential operators. Starting from the -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.
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