arXiv subjects

H. F. Goenner

Publications and source records attributed to H. F. Goenner.

4 recordsLinked to original sources

arXiv2004

Concerning the generalized Lorentz symmetry and the generalization of the Dirac equation

The work is devoted to the generalization of the Dirac equation for a flat locally anisotropic, i.e., Finslerian space-time. At first we reproduce the corresponding metric and a group of the generalized Lorentz transformations, which has the meaning of the relativistic symmetry group of such event space. Next, proceeding from the requirement of the generalized Lorentz invariance we find a generalized Dirac equation in its explicit form. An exact solution of the nonlinear generalized Dirac equation is also presented.

hep-th↗

arXiv1999

Finslerian spaces possessing local relativistic symmetry

It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $γ>5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence of the GZK cutoff), has a nontrivial solution. Its essence consists in the discovery of the so-called generalized Lorentz transformations which seem to correctly link the inertial reference frames at any values of $γ.$ Like the usual Lorentz transformations, the generalized ones are linear, possess group properties and lead to the Einstein law of addition of 3-velocities. However, their geometric meaning turns out to be different: they serve as relativistic symmetry transformations of a flat anisotropic Finslerian event space rather than of Minkowski space. Consideration is given to two types of Finsler spaces which generalize locally isotropic Riemannian space-time of relativity theory, e. g. Finsler spaces with a partially and entirely broken local 3D isotropy. The investigation advances arguments for the corresponding generalization of the theory of fundamental interactions and for a specific search for physical effects due to local anisotropy of space-time.

gr-qc↗

arXiv1998

On a Possibility of Phase Transitions in the Geometric Structure of Space-Time

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase transitions in its geometric structure. These transitions together with the evolution of each of the possible metric states make up the general picture of space-time manifold dynamics.

gr-qc↗

arXiv1997

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 Poincaré (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.

gr-qc↗