Limiting Case of Modified Electroweak Model for Contracted Gauge Group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction, clarified motivatio

Higgsless Electroweak Model and Contraction of Gauge Group

A modified formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The {\it free} Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same experimentally verified fields with the same masses as the Standard Electroweak Model. The vector bosons masses are automatically generated, so there is no need in special mechanism of spontaneous symmetry breaking. The limiting case of the modified Higgsless Electroweak Model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson, electromagnetic and electron fields are interpreted as an external ones with respect to W-bosons and neutrino fields. The W-bosons and neutrino fields do not effect on these external fields. The masses of all particles remain the same, but the field interactions in contracted model are more simple as compared with the standard Electroweak Model due to nullification of some terms.Comment: Talk at the International Workshop "`Supersymmetries and Quantum Symmetries"' (SQS-09), Dubna, Russia, July 29 -- August 3, 2009, 11

Noncommutative space-time models

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N=5 part of them are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.Comment: 8 pages; talk given at XIV International Colloquium of Integrable Systems, Prague, June 16-18, 200

Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis

Spaces of constant curvature and their motion groups are described most naturally in Cartesian basis. All these motion groups also known as CK groups are obtained from orthogonal group by contractions and analytical continuations. On the other hand quantum deformation of orthogonal group $SO(N)$ is most easily performed in so-called symplectic basis. We reformulate its standard quantum deformation to Cartesian basis and obtain all possible contractions of quantum orthogonal group $SO_q(N)$ both for untouched and transformed deformation parameter. It turned out, that similar to undeformed case all CK contractions of $SO_q(N)$ are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of $SO_q(N), N=3,4,5$ are regarded as an examples.Comment: The statement of the basic theorem have correct. 30 pages, Latex. Report given at X International Conference on Symmetry Methods in Physics, August 13-19, 2003, Yerevan, Armenia. Submitted in Journal Physics of Atomic Nucle

Possible contractions of quantum orthogonal groups

Possible contractions of quantum orthogonal groups which correspond to different choices of primitive elements of Hopf algebra are considered and all allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations of kinematical groups have been investigated and have shown that quantum analog of (complex) Galilei group G(1,3) do not exist in our scheme.Comment: 10 pages, Latex. Report given at XXIII Int. Colloquium on Group Theoretical Methods in Physics, July 31- August 5, 2000, Dubna (Russia

On contractions of classical basic superalgebras

We define a class of orthosymplectic $osp(m;j|2n;\omega)$ and unitary $sl(m;j|n;\epsilon)$ superalgebras which may be obtained from $osp(m|2n)$ and $sl(m|n)$ by contractions and analytic continuations in a similar way as the special linear, orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Casimir operators of Cayley-Klein superalgebras are obtained from the corresponding operators of the basic superalgebras. Contractions of $sl(2|1)$ and $osp(3|2)$ are regarded as an examples.Comment: 15 pages, Late

On the Fermionic Frequencies of Circular Strings

We revisit the semiclassical computation of the fluctuation spectrum around different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from the Green-Schwarz action. It has been known that the results for these frequencies obtained from the algebraic curve and from the worldsheet computations sometimes do not agree. In particular, different methods give different results for the half-integer shifts in the mode numbers of the frequencies. We find that these discrepancies can be removed if one carefully takes into account the transition matrices in the spin bundle over the target space.Comment: 13 pages, 1 figur