118 research outputs found

### 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

### 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

### General Very Special Relativity is Finsler Geometry

We ask whether Cohen and Glashow's Very Special Relativity model for Lorentz
violation might be modified, perhaps by quantum corrections, possibly producing
a curved spacetime with a cosmological constant. We show that its symmetry
group ISIM(2) does admit a 2-parameter family of continuous deformations, but
none of these give rise to non-commutative translations analogous to those of
the de Sitter deformation of the Poincar\'e group: spacetime remains flat. Only
a 1-parameter family DISIM_b(2) of deformations of SIM(2) is physically
acceptable. Since this could arise through quantum corrections, its
implications for tests of Lorentz violations via the Cohen-Glashow proposal
should be taken into account. The Lorentz-violating point particle action
invariant under DISIM_b(2) is of Finsler type, for which the line element is
homogeneous of degree 1 in displacements, but anisotropic. We derive
DISIM_b(2)-invariant wave equations for particles of spins 0, 1/2 and 1. The
experimental bound, $|b|<10^{-26}$, raises the question ``Why is the
dimensionless constant $b$ so small in Very Special Relativity?''Comment: 4 pages, minor corrections, references adde

### 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

### On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term

A (n + 1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For
diagonal cosmological-type metrics, the equations of motion are reduced to a
set of Lagrange equations. The effective Lagrangian contains two
"minisuperspace" metrics on R^n. The first one is the well-known 2-metric of
pseudo-Euclidean signature and the second one is the Finslerian 4-metric that
is proportional to n-dimensional Berwald-Moor 4-metric. When a
"synchronous-like" time gauge is considered the equations of motion are reduced
to an autonomous system of first-order differential equations. For the case of
the "pure" Gauss-Bonnet model, two exact solutions with power-law and
exponential dependence of scale factors (with respect to "synchronous-like"
variable) are obtained. (In the cosmological case the power-law solution was
considered earlier in papers of N. Deruelle, A. Toporensky, P. Tretyakov and S.
Pavluchenko.) A generalization of the effective Lagrangian to the Lowelock case
is conjectured. This hypothesis implies existence of exact solutions with
power-law and exponential dependence of scale factors for the "pure" Lowelock
model of m-th order.Comment: 24 pages, Latex, typos are eliminate

### 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

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