13 research outputs found
-Minkowski star product in any dimension from symplectic realization
We derive an explicit expression for the star product reproducing the
-Minkowski Lie algebra in any dimension . The result is obtained by
suitably reducing the Wick-Voros star product defined on
with . It is thus shown that the new star
product can be obtained from a Jordanian twist.Comment: published versio
-Deformations and Extended -Minkowski Spacetimes
We extend our previous study of Hopf-algebraic -deformations of all
inhomogeneous orthogonal Lie algebras as written in a tensorial
and unified form. Such deformations are determined by a vector which for
Lorentzian signature can be taken time-, light- or space-like. We focus on some
mathematical aspects related to this subject. Firstly, we describe real forms
with connection to the metric's signatures and their compatibility with the
reality condition for the corresponding -Minkowski (Hopf) module
algebras. Secondly, -adic vs -analog (polynomial) versions of deformed
algebras including specialization of the formal deformation parameter
to some numerical value are considered. In the latter the general covariance is
lost and one deals with an orthogonal decomposition. The last topic treated in
this paper concerns twisted extensions of -deformations as well as the
description of resulting noncommutative spacetime algebras in terms of solvable
Lie algebras. We found that if the type of the algebra does not depend on
deformation parameters then specialization is possible.Comment: new extended version with new material added and with title change
Gauge Theory on Twisted -Minkowski: Old Problems and Possible Solutions
We review the application of twist deformation formalism and the construction
of noncommutative gauge theory on -Minkowski space-time. We compare two
different types of twists: the Abelian and the Jordanian one. In each case we
provide the twisted differential calculus and consider gauge theory.
Different methods of obtaining a gauge invariant action and related
problems are thoroughly discussed