Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants

It is shown that the group of generalized Lorentz transformations serves as relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous breaking of initial gauge symmetry and from the formation of anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables exact taking into account the influence of condensate on the dynamics of fundamental fields. In particular, the corresponding generalized Dirac equation turns out to be nonlinear. We have found two noncompact subgroups of the group of generalized Lorentz symmetry and their geometric invariants. These subgroups play a key role in constructing exact solutions of such equation.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A class of anisotropic (Finsler-) space-time geometries

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of isometries. These turn out to be isomorphic to subgroups of the Poincar\'e (Lorentz-) group complemented by the generator of a dilatation. The arising Finsler geometries may be used for the construction of relativistic theories testing the isotropy of space. It is shown that the Finsler space with the only preferred null direction is the anisotropic space closest to isotropic Minkowski-space of the full class discussed.Comment: 12 pages, latex, no figure

Relativity principles in 1+1 dimensions and differential aging reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient $\beta$, special relativity being recovered for $\beta=0$. The effect of differential aging is studied for the different values of $\beta$. Below the critical values $|\beta| =1/c$ the differential aging has the usual direction - after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical values the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.Comment: 12 pages, no figures. Previous title "Parity violating terms in clocks' behavior and differential aging reversal". v2: shortened introduction, some sections removed, pointed out the relation with Finsler metrics. Submitted to Found. Phys. Let

OPERA superluminal neutrinos and Kinematics in Finsler spacetime

The OPERA collaboration recently reported that muon neutrinos could be superluminal. More recently, Cohen and Glashow pointed that such superluminal neutrinos would be suppressed since they lose their energies rapidly via bremsstrahlung. In this Letter, we propose that Finslerian nature of spacetime could account for the superluminal phenomena of particles. The Finsler spacetime permits the existence of superluminal behavior of particles while the casuality still holds. A new dispersion relation is obtained in a class of Finsler spacetime. It is shown that the superluminal speed is linearly dependent on the energy per unit mass of the particle. We find that such a superluminal speed formula is consistent with data of OPERA, MINOS and Fermilab-1979 neutrino experiments as well as observations on neutrinos from SN1987a.Comment: 10 pages, 2 figures. Viewpoints of Finslerian special relativity on OPERA superluminal neutrino

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.Comment: 35 pages, 5 figures, to appear in the Russian journal Hypercompl. Numb. Geom. Phys; submit/0362894 (George Bogoslovsky

Design and Status of the Dipole Spectrometer Magnet for the ALICE Experiment

Proposal of abstract for MT16, Tallahesse, Florida, 26th September to 2nd October 1999.A large Dipole Magnet is required for the Muon Arm Spectrometer of the ALICE experiment at the LHC.The absence of strong requirements on the symmetry and homogeneity of the magnetic field has lead to a design dominated by economic and feasibility considerations.In March 1997 the decision was taken to build a resistive dipole magnet for the muon spectrometer of the ALICE experiment. Since then, design work has been pursued in JINR/Russia and at CERN. While a common concept has been adopted for the construction of the steel core, two different proposals have been made for the manufacturing technology of the excitation coils. In both cases, however, the conductor material will be Aluminium.The general concept of the dipole magnet is based on a window frame return yoke, fabricated from low carbon steel sheets. The flat vertical poles follow the defined acceptance angle of 9 degrees. The excitation coils are of saddle type. The coils are wound from large hollow Aluminium profiles. They are cooled by pressurized demineralised water. The coil ends are located to both sides of the magnet yoke and determine the overall length of the magnet. The main flux direction in the gap is horizontal and perpendicular to the LHC beam axis.Both coil concepts and the underlying manufacturing technology are compared and the present status of the development of the magnet is described