相关论文: Finslerian spaces possessing local relativistic sy…
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…
Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…
Within the framework of the Finslerian approach to the problem of violation of Lorentz symmetry, consideration is given to a flat axially symmetric Finslerian space of events, which is the generalization of Minkowski space. Such an event…
Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest…
We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature.…
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…
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 Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a…
In my previous work, physics/0205011, I reported several observations on special relativity, its experimental facts and its relations to quantum mechanics and statistical mechanics. These observations made us conscious: Special relativity…
Ever since the work of von Ignatowsky circa 1910 it has been known (if not always widely appreciated) that the relativity principle, combined with the basic and fundamental physical assumptions of locality, linearity, and isotropy, leads…
We study the geometric phase transitions that accompany the dynamic rearrangement of vacuum under spontaneous violation of initial gauge symmetry. The rearrangement may give rise to condensates of three types, namely the scalar, axially…
Upon straightforward four--directional extension of the special--relativistic two--dimensional transformations to the four--dimensional case we lead to convenient totally anisotropic kinematic transformations, which prove to reveal many…
It is shown that in the case of spontaneous breaking of the original gauge symmetry, a dynamic rearrangement of vacuum may lead to the formation of some anisotropic condensates. The appearance of such condensates causes the respective phase…
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
In this work, we study the symmetries of a Lorentz violating bipartite-Finsler spacetime. By using the Finslerian Killing equation for the bipartite-Finsler metric, we analyze how the anisotropy of the bipartite spacetime modifies the local…
Finsler geometry serves as a fundamental and natural extension of Riemannian geometry, providing a valuable framework for investigating Lorentz violation in spacetime. Previous studies have treated the Finsler structures associated with…
Within all approaches to quantum gravity small violations of the Einstein Equivalence Principle are expected. This includes violations of Lorentz invariance. While usually violations of Lorentz invariance are introduced through the coupling…
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A…
We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined…
Finslerian extensions of Special and General Relativity -- commonly referred to as Very Special and Very General Relativity -- necessitate the development of a unified Lorentz-Finsler geometry. However, the scope of this geometric framework…