摘要:

The (left coalgebra) line bundle associated to the quantum Hopf fibration of any quantum two-sphere is shown to be a finitely generated projective module. The corresponding projector is constructed and its monopole charge is computed. It is shown that the Diracq-monopole connection on any quantum two-sphere induces the Grassmannian connection built with this projector. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57118

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Using the fact that the algebraM≐MN(C)ofN×Ncomplex matrices can be considered as a reduced quantum plane, and that it is a module algebra for a finite dimensional Hopf algebra quotientHofUqsl(2)whenqis a root of unity, we reduce this algebraMof matrices (assumingNodd) into indecomposable modules forH. We also show how the same finite dimensional quantum group acts on the space of generalized differential forms defined as the reduced Wess Zumino complex associated with the algebraM. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57119

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We consider the construction of explicit solutions of a hierarchy of q-deformed equations which are (conditionally) quantum conformal invariant. We give two types of solutions—polynomial solutions and solutions in terms of q-deformation of the plane wave. We give a q-deformation of the plane wave as a formal power series in the noncommutative coordinates of q-Minkowski space-time and four-momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d’Alembert equation on the q-Lorentz covariant momentum cone. On the other hand, this q-plane wave is not an exponent or q-exponent. Thus, it differs conceptually from the classical plane wave and may serve as a its regularization. Using this we give also solutions of the massless Dirac equation involving two conjugated q-plane waves—one for the neutrino, the other for the antineutrino. It is also interesting that the neutrino solutions are deformed only through the q-pane wave, while the prefactor is classical. Thus, we can speak of a definite left-right asymmetry of the quantum conformal deformation of the neutrino‐antineutrino system. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57120

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A general discussion is given of reality conditions within the context of noncommutative geometry. In particular a real differential calculus is constructed over the quantum euclidean planes. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57121

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We present briefly the deformation philosophy and indicate, with references, how it was applied to the quantization of Nambu mechanics and to particle physics in anti De Sitter space. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57112

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classicalr-matrices, classical Yang-Baxter equations (CYBE), Fro¨benius algebras and parabolic subalgebras. Then we construct the quantum deformation ofD=1,D=2andD=3conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization ofD=4conformal algebra. We build three classes ofsl(4,C)classicalr-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensionalr-matrices allow to impose theD=4conformalo(4,2)≃su(2,2)reality conditions. Weyl reflections and Dynkin diagram automorphisms foro(4,2)define the class of admissible bases for given classicalr-matrices. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57114

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The deformed double covering ofE(2)group, denoted byE˜&kgr;(2),is obtained by contraction from theSU&mgr;(2).The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant calculus on bothE˜&kgr;(2)and the deformed Euclidean groupE&kgr;(2)and two different 4D-bicovariant calculi onE˜&kgr;(2)which correspond to the one 4D-bicovariant calculi onE&kgr;(2)described in Ref. [7]. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57115

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Few new twisting elements for extended jordanian quantization ofsl(N),for the Drinfeld-Jimbo quantum algebraUq(sl(3)),and for the Lie superalgebraosp(1|2)are given. Applications of these twisting elements to the spin chain models integrable by the quantum inverse scattering method are discussed. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57116

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of well-defined scalar product is considered. An example of physical effect in system with generalized statistics is also given. ©1998 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.57122

出版商:AIP    

年代:1998

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.57123

出版商:AIP    

年代:1998

数据来源: AIP