7 research outputs found
-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
We consider -deformed relativistic quantum phase space and possible
implementations of the Lorentz algebra. There are two ways of performing such
implementations. One is a simple extension where the Poincar\'e algebra is
unaltered, while the other is a general extension where the Poincar\'e algebra
is deformed. As an example we fix the Jordanian twist and the corresponding
realization of noncommutative coordinates, coproduct of momenta and addition of
momenta. An extension with a one-parameter family of realizations of the
Lorentz generators, dilatation and momenta closing the Poincar\'e-Weyl algebra
is considered. The corresponding physical interpretation depends on the way the
Lorentz algebra is implemented in phase space. We show how the spectrum of the
relativistic hydrogen atom depends on the realization of the generators of the
Poincar\'e-Weyl algebra.Comment: Title changed and minor changes in the tex
Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
We propose a generalized description for the kappa-Poincare-Hopf algebra as a
symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate
all the possible implementations of (deformed) Lorentz algebras which are
compatible with the given choice of kappa-Minkowski algebra realization. For
the given realization of kappa-Minkowski spacetime there is a unique
kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. We have
constructed a three-parameter family of deformed Lorentz generators with
kappa-Poincare algebras which are related to kappa-Poincare-Hopf algebra with
undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra are
obtained as special cases. Also deformation of igl(4) Hopf algebra compatible
with the kappa-Minkowski spacetime is presented. Some physical applications are
briefly discussed.Comment: 15 pages; journal version; Physics Letters B (2012
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