Note on Finslerian relativity

Ishikawa, Hirohisa

doi:10.1063/1.525021

Cited by 40 publications

(32 citation statements)

References 27 publications

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“…The dependence on the fiber coordinates y a directly reflects the Lorentz violating structure of the Finslerian space-time. They may be physically interpreted as an arbitrary direction at each tangent space induced by the breaking of Lorentz invariance (see for example [110,112]). In fact, Finsler geometry is encountered in Lorentz violating branches of quantum gravity [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101] and also effectively describes motion in anisotropic media [113,114].…”

Section: Finsler Geometrymentioning

confidence: 99%

Cosmic magnetization in curved and Lorentz violating space–times

Kouretsis

2014

Eur. Phys. J. C

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The presence of the large-scale magnetic fields is one of the greatest puzzles of contemporary cosmology. The symmetries of the electromagnetic field theory combined with the geometric structure of the FRW universe leads to an adiabatic decay of the primordial magnetic fields. Due to this rapid decay the residual large-scale magnetic field is astrophysically unimportant. A common feature among many of the proposed amplification mechanisms is the violation of Lorentz symmetries. We introduce an amplification mechanism within a Lorentz violating environment where we use Finsler geometry as our theoretical background. The mechanism is based on the adoption of a local anisotropic structure that leads to modifications on the Ricci identities. Thus, the wave-like equation of any vector source, including the magnetic field, is enriched by the Finslerian curvature theory. In particular limits, the remaining seed field can be strong enough to seed the galactic dynamo. In our analysis we also develop the 1+3 covariant formalism for the 4-vector potential in curved space-times.

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Section: Finsler Geometrymentioning

confidence: 99%

Cosmic magnetization in curved and Lorentz violating space–times

Kouretsis

2014

Eur. Phys. J. C

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“…The concept of local anisotropy is largely used in some divisions of theoretical and mathematical physics [121,56,57,78] (see also possible applications in physics and biology in [6,5]). The first models of locally anisotropic (la) spaces (la-spaces) have been proposed by P.Finsler [38] and E.Cartan [29] (early approaches and modern treatments of Finsler geometry and its extensions can be found, for instance, in [90,7,8,74]).…”

Section: Introductionmentioning

confidence: 99%

Superstrings in higher order extensions of Finsler superspaces

Vacaru

1997

Nuclear Physics B

208

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The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern KaluzaKlein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on higher order fiber bundles provided with nonlinear and distingushed connections and metric structures. The view adopted here is that a general field theory should incorporate all possible anisotropic and stochastic manifestations of classical and quantum interactions and, in consequence, a corresponding modification of basic principles and mathematical methods in formulation of physical theories.The presentation is divided into two parts. The first five sections cover the higher order anisotropic superspaces. We focus on the geometry of distinguished by nonlinear connection vector superbundles, consider different supersymmetric extensions of Finsler and Lagrange spaces and analyze the structure of basic geometric objects on such superspaces. The remaining five sections are devoted to the theory of higher order anisotropic superstrings. In the framework of supersymmetric nonlinear sigma models in Finser extended backgrounds we prove that the lowenergy dynamics of such strings contains motion equations for locally anisotropic field interactions.Our work is to be compared with important previous variants of extension of Finsler geometry and gravity (see, for instance, [7,76,74,14]). There are substantial differences, because we rely on modeling of higher order anisotropic interactions on superbundle spaces and do not propose 1 some "exotic" Finsler models but a general approach which for trivial or corresponding parametization of nonlinear connection stuctures reduces to Kaluza-Klein and another variants of compactified higher-dimension space-times. The geometry of nonlinear connections (not being confused with connections for nonlinear realizations of gauge supergroups) is firstly considered for superspaces and possible cosequences on nonlinear connection field for compatible propagations of strings in anisotropic backgrounds are analyzed.Finally, we note that the developed computation methods are general (in some line very similar to those for Einstein-Cartan-Weyl spaces which is a priority comparing with another combersome calculations in Finsler geometry) and admit extension to various Clifford and spinor bundles.

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“…15 On the other hand, it is a natural choice, since the expressions appearing in the formulation of Fermat's principle, the second variation formula and the Morse index theorem must be evaluated along the curves λ: I → M at (λ(s),λ(s)).…”

Section: Discussionmentioning

confidence: 99%

On Fermat's principle for causal curves in time oriented Finsler spacetimes

Torromé

Piccione

Vitório

2012

Journal of Mathematical Physics

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In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the second variation of the time arrival functional along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented. C 2012 American Institute of Physics.This notion of reversibility is different from the one considered by Beem 3 and also different than the one considered in Ref. 25. Our definition of reversible metric is stronger than the corresponding notions of Beem and that the one considered in the theory of Pfeifer-Wohlfart. B. Elementary causality notions for Finsler spacetimesThe fundamental causal notions of a Finsler spacetime (M, L) is a natural generalization of the Lorentzian causal framework. 4 A vector field X ∈ TM is said to be timelike if L(x, X(x)) < 0 at all points x ∈ M and a curve λ : I −→ M is timelike if the tangent vector field is timelike L(λ(s),λ(s)) < 0. A vector field X ∈ is lightlike if L(x, X(x)) = 0, ∀x ∈ M; a curve is lightlike if its tangent vector field is lightlike. Similar notions hold for spacelike vector and curves. A curve is causal if it is either timelike and has constant speed g˙λ(λ,λ) := L(λ,λ) = g i j (λ, T )λ iλ j or if it is lightlike.The following facts can be proved from the definition of Finsler spacetime.

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Note on Finslerian relativity

Cited by 40 publications

References 27 publications

Cosmic magnetization in curved and Lorentz violating space–times

Cosmic magnetization in curved and Lorentz violating space–times

Superstrings in higher order extensions of Finsler superspaces

On Fermat's principle for causal curves in time oriented Finsler spacetimes

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