675 research outputs found
Quasi Exactly Solvable 22 Matrix Equations
We investigate the conditions under which systems of two differential
eigenvalue equations are quasi exactly solvable. These systems reveal a rich
set of algebraic structures. Some of them are explicitely described. An exemple
of quasi exactly system is studied which provides a direct counterpart of the
Lam\'e equation.Comment: 14 pages, Plain Te
Projective representation of k-Galilei group
The projective representations of k-Galilei group G_k are found by
contracting the relevant representations of k-Poincare group. The projective
multiplier is found. It is shown that it is not possible to replace the
projective representations of G_k by vector representations of some its
extension.Comment: 15 pages Latex fil
Canonical and Lie-algebraic twist deformations of -Poincare and contractions to -Galilei algebras
We propose canonical and Lie-algebraic twist deformations of
-deformed Poincare Hopf algebra which leads to the generalized
-Minkowski space-time relations. The corresponding deformed
-Poincare quantum groups are also calculated. Finally, we perform the
nonrelativistic contraction limit to the corresponding twisted Galilean
algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal,
v2: submitted incidentally, v4: the page numbers for all references in
preprint version are provide
Scalar field propagation in the phi^4 kappa-Minkowski model
In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model
based on the kappa-deformed star product, ({*}_h). The action is modified by
expanding up to linear order in the kappa-deformation parameter a, producing an
effective model on commutative spacetime. For the computation of the tadpole
diagram contributions to the scalar field propagation/self-energy, we
anticipate that statistics on the kappa-Minkowski is specifically
kappa-deformed. Thus our prescription in fact represents hybrid approach
between standard quantum field theory (QFT) and NCQFT on the kappa-deformed
Minkowski spacetime, resulting in a kappa-effective model. The propagation is
analyzed in the framework of the two-point Green's function for low,
intermediate, and for the Planckian propagation energies, respectively.
Semiclassical/hybrid behavior of the first order quantum correction do show up
due to the kappa-deformed momentum conservation law. For low energies, the
dependence of the tadpole contribution on the deformation parameter a drops out
completely, while for Planckian energies, it tends to a fixed finite value. The
mass term of the scalar field is shifted and these shifts are very different at
different propagation energies. At the Planckian energies we obtain the
direction dependent kappa-modified dispersion relations. Thus our
kappa-effective model for the massive scalar field shows a birefringence
effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected.
Shorter version of the paper arXiv:1107.236
Quantum double and -Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory
We review the role of Drinfeld doubles and kappa-Poincare symmetries in
quantised (2+1)-gravity and Chern-Simons theory. We discuss the conditions
under which a given Hopf algebra symmetry is compatible with a Chern-Simons
theory and determine this compatibility explicitly for the Drinfeld doubles and
kappa-Poincare symmetries associated with the isometry groups of (2+1)-gravity.
In particular, we explain that the usual kappa-Poincare symmetries with a
timelike deformation are not directly associated with (2+1)-gravity. These
kappa-Poincare symmetries are linked to Chern-Simons theory only in the de
Sitter case, and the relevant Chern-Simons theory is physically inequivalent to
(2+1)-gravity.Comment: 11 pages, no figures, expanded version of talk at the conference
Theory Canada 4, references and explanations added, typos correcte
q-Deformed Superalgebras
The article deals with q-analogs of the three- and four-dimensional Euclidean
superalgebra and the Poincare superalgebra.Comment: 38 pages, LateX, no figures, corrected typo
-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
The -deformed Poincar{\'e} superalgebra written in Hopf
superalgebra form is transformed to the basis with classical Lorentz subalgebra
generators. We show that in such a basis the -deformed Poincare
superalgebra can be written as graded bicrossproduct. We show that the
-deformed superalgebra acts covariantly on -deformed
chiral superspace.Comment: 13 pages, late
Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
We study systematically, through two loops, the divergence structure of the
supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By
introducing a spurion field to represent the supersymmetry breaking term F^3 we
are able to perform our calculations using conventional supergraph techniques.
Divergent terms proportional to F, F^2 and F^3 are produced (the first two are
to be expected on general grounds) but no higher-point divergences are found.
By adding ab initio F and F^2 terms to the original lagrangian we render the
model renormalizable. We determine the renormalization constants and beta
functions through two loops, thus making it possible to study the
renormalization group flow of the nonanticommutation parameter.Comment: 36 pages, 25 figures, Latex fil
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