164 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
Quantum field theory in generalised Snyder spaces
We discuss the generalisation of the Snyder model that includes all possible
deformations of the Heisenberg algebra compatible with Lorentz invariance and
investigate its properties. We calculate peturbatively the law of addition of
momenta and the star product in the general case. We also undertake the
construction of a scalar field theory on these noncommutative spaces showing
that the free theory is equivalent to the commutative one, like in other models
of noncommutative QFT.Comment: 12 pages. arXiv admin note: substantial text overlap with
arXiv:1608.0620
The Energy Operator for a Model with a Multiparametric Infinite Statistics
In this paper we consider energy operator (a free Hamiltonian), in the
second-quantized approach, for the multiparameter quon algebras:
with
any hermitian matrix of deformation parameters. We obtain
an elegant formula for normally ordered (sometimes called Wick-ordered) series
expansions of number operators (which determine a free Hamiltonian). As a main
result (see Theorem 1) we prove that the number operators are given, with
respect to a basis formed by "generalized Lie elements", by certain normally
ordered quadratic expressions with coefficients given precisely by the entries
of the inverses of Gram matrices of multiparticle weight spaces. (This settles
a conjecture of two of the authors (S.M and A.P), stated in [8]). These Gram
matrices are hermitian generalizations of the Varchenko's matrices, associated
to a quantum (symmetric) bilinear form of diagonal arrangements of hyperplanes
(see [12]). The solution of the inversion problem of such matrices in [9]
(Theorem 2.2.17), leads to an effective formula for the number operators
studied in this paper. The one parameter case, in the monomial basis, was
studied by Zagier [15], Stanciu [11] and M{\o}ller [6].Comment: 24 pages. accepted in J. Phys. A. Math. Ge
Classical dynamics on curved Snyder space
We study the classical dynamics of a particle in nonrelativistic Snyder-de
Sitter space. We show that for spherically symmetric systems, parametrizing the
solutions in terms of an auxiliary time variable, which is a function only of
the physical time and of the energy and angular momentum of the particles, one
can reduce the problem to the equivalent one in classical mechanics. We also
discuss a relativistic extension of these results, and a generalization to the
case in which the algebra is realized in flat space.Comment: 12 pages, LaTeX, version published on CQ
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
Example of q-deformed Field Theory
The non-relativistic Chern-Simons theory with the single-valued anyonic field
is proposed as an example of q-deformed field theory. The corresponding
q-deformed algebra interpolating between bosons and fermions,both in position
and momentum spaces, is analyzed.A possible generalization to a space with an
arbitrary dimension is suggested.Comment: 13 pages,LaTe
New realizations of Lie algebra kappa-deformed Euclidean space
We study Lie algebra -deformed Euclidean space with undeformed
rotation algebra and commuting vectorlike derivatives. Infinitely
many realizations in terms of commuting coordinates are constructed and a
corresponding star product is found for each of them. The -deformed
noncommutative space of the Lie algebra type with undeformed Poincar{\'e}
algebra and with the corresponding deformed coalgebra is constructed in a
unified way.Comment: 30 pages, Latex, accepted for publication in Eur.Phys.J.C, some typos
correcte
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