Quantum deformations of conformal algebras with mass-like deformation parameters

Journal Article · Tue Dec 15 04:00:00 EST 1998 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.57114· OSTI ID:21202687

Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek ^[1]; Minnaert, Pierre ^[2]

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1. Institute for Theoretical Physics, University of Wroclaw, 50-204 Wroclaw (Poland)
2. Laboratoire de Physique Theorique, Universite Bordeaux 1, 33-175 Gradignan (France)

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2) reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.

• OSTI ID: 21202687
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 453; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
CONFORMAL INVARIANCE
FIELD EQUATIONS
GEOMETRY
LIE GROUPS
QUANTIZATION
QUANTUM FIELD THEORY
R MATRIX
REST MASS
SYMMETRY