12 research outputs found
Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
We investigate the properties of kappa-Minkowski spacetime by using
representations of the corresponding deformed algebra in terms of undeformed
Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare
algebra extended with the generators of the deformed Weyl algebra. The part of
deformed algebra, generated by rotation, boost and momentum generators, is
described by the Hopf algebra structure. The approach used in our
considerations is completely Lorentz covariant. We further use an adventages of
this approach to consistently construct a star product which has a property
that under integration sign it can be replaced by a standard pointwise
multiplication, a property that was since known to hold for Moyal, but not also
for kappa-Minkowski spacetime. This star product also has generalized trace and
cyclic properties and the construction alone is accomplished by considering a
classical Dirac operator representation of deformed algebra and by requiring it
to be hermitian. We find that the obtained star product is not translationally
invariant, leading to a conclusion that the classical Dirac operator
representation is the one where translation invariance cannot simultaneously be
implemented along with hermiticity. However, due to the integral property
satisfied by the star product, noncommutative free scalar field theory does not
have a problem with translation symmetry breaking and can be shown to reduce to
an ordinary free scalar field theory without nonlocal features and tachionic
modes and basicaly of the very same form. The issue of Lorentz invariance of
the theory is also discussed.Comment: 22 pages, no figures, revtex4, in new version comments regarding
translation invariance and few references are added, accepted for publication
in Int. J. Mod. Phys.
Kappa-deformed Snyder spacetime
We present Lie-algebraic deformations of Minkowski space with undeformed
Poincare algebra. These deformations interpolate between Snyder and
kappa-Minkowski space. We find realizations of noncommutative coordinates in
terms of commutative coordinates and derivatives. Deformed Leibniz rule, the
coproduct structure and star product are found. Special cases, particularly
Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. Our
construction leads to a new class of deformed special relativity theories.Comment: 12 pages, no figures, LaTeX2e class file, accepted for publication in
Modern Physics Letters
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
Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of
non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras.
We prove that every contracted QUEA in a certain class is a cochain twist of
the corresponding undeformed universal envelope. Consequently, these contracted
QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we
consider kappa-Poincare in 3 and 4 spacetime dimensions.Comment: 32 page
Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
We deform Heisenberg algebra and corresponding coalgebra by twist. We present
undeformed and deformed tensor identities. Coalgebras for the generalized
Poincar\'{e} algebras have been constructed. The exact universal -matrix for
the deformed Heisenberg (co)algebra is found. We show, up to the third order in
the deformation parameter, that in the case of -Poincar\'{e} Hopf
algebra this -matrix can be expressed in terms of Poincar\'{e} generators
only. This implies that the states of any number of identical particles can be
defined in a -covariant way.Comment: 10 pages, revtex4; discussion enlarged, references adde