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

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

The Quantum Symplectic Cayley-Klein Groups

The contraction method applied to the construction of the nonsemisimple quantum symplectic Cayley-Klein groups $Fun(Sp_q(n;j))$. This groups has been realised as Hopf algebra of the noncommutative functions over the algebra with nilpotent generators. The dual quantum algebras $sp_q(n;j)$ are constructed.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phy

Contractions of Integrable Equations

The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phy

GHz sandwich strip inductors based on Fe-N Films

Planar strip inductors consisting of two Fe-N films enclosing a conducting film made of Cu, were fabricated on oxidized Si substrates. The inductors were 1mm long, 2 to 100 um wide, with layers of thickness ~0.1 um for the magnetic films and ~0.5 um for the conductor. The soft (Hc=4-8 Oe) magnetic layers were biased during impedance measurement by applying an external field along the strip length thereby facilitating the transverse susceptibility configuration. Biased strips exhibited 70 to 100% inductance enhancement at 1GHz with quality factors Q=4.5 to 3, respectively. The magnetic contribution to the total flux in the narrow devices was less than predicted theoretically, which was attributed to hardening of the magnetic material at the edges of the strip, where the deposition was close to 60 degree incidence. Test films were fabricated on tilted substrates and found to develop a very high anisotropy (up to 1 kOe) for deposition angles larger than 30 degrees. Optimizing the flux closure at the strip edges and using thicker conductor layers is essential for further improving the performance of sandwich strip inductors.Comment: 18 pages, 9 figure