https://doi.org/10.1140/epjc/s10052-017-4786-9
Regular Article - Theoretical Physics
Quantizations of
Lorentz symmetry
1
Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50-205, Wrocław, Poland
2
Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow, 119991, Russian Federation
* e-mail: jerzy.lukierski@ift.uni.wroc.pl
Received:
27
February
2017
Accepted:
22
March
2017
Published online:
11
April
2017
Using the isomorphism we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r-matrices) for real forms
and
of the complex Lie algebra
in terms of real forms of
:
,
and
. We prove that the
Lorentz symmetry
has three different Hopf-algebraic quantum deformations, which are expressed in the simplest way by two standard
and
q-analogs and by simple Jordanian
twist deformation. These quantizations are presented in terms of the quantum Cartan–Weyl generators for the quantized algebras
and
as well as in terms of quantum Cartesian generators for the quantized algebra
. Finally, some applications of the deformed
Lorentz symmetry are mentioned.
© The Author(s), 2017