arXiv subjects

G. S. Asanov

Publications and source records attributed to G. S. Asanov.

28 records · Page 2Linked to original sources

arXiv2005

Finsleroid--Relativistic Time--Asymmetric Space and Quantized Fields

For well-defined Finsleroid-relativistic space $\cE_g^{SR}$ (with the upperscript SR meaning Special-Relativistic) due only to accounting a characteristic parameter $g$ which measures the deviation of the geometry from its pseudoeuclidean precursor, the creation of the respective quantization programs for relativistic physical fields seems to be an urgent task. The parameter may take on the values over all the real range; at $g=0$ the space is reduced to become an ordinary pseudoeuclidean one. In the present work, the formulation of theory for relativistic physical fields in such a space is initiated. A general method to solve respective scalar, electromagnetic, and spinor field equations is proposed basing on the conformal flatness. At any value of the parameter, the expansion of the relativistic fields with respect to non-plane waves appeared is found, which proposes a base upon which the fields can be quantized in context of the Finsleroid-relativistic approach. Remarkably, the regulators can naturally be proposed to overcome divergences in relativistic field integrals. The respective key and basic concepts involved are presented. For short, the abbreviations FMF, FMT, and FHF will be used for the Finsleroid-relativistic metric function, the associated metric tensor, and the associated Hamiltonian function, respectively.

math-ph↗

arXiv2004

Finsleroid--Relativistic Space Endowed With Scalar Product

When a single time-like vector is distinguished geometrically to present the only preferred direction in extending the pseudoeuclidean geometry, the hyperboloid may not be regarded as an exact carrier of the unit-vector image. So under respective conditions one may expect that some time-assymetric figure should be substituted with the hyperboloid. To this end we shall use the pseudo-Finsleroid. The spatial-rotational invariance (the P-parity) is retained. The constant negative curvature is the fundamental property of the pseudo-Finsleroid surface. The present paper develops the approach in the direction of evidencing the concepts of angle, scalar product, and geodesics. In Appendices we shortly outline the basic aspects that stem from the choice of the Finsleroid-relativistic metric functions.

math-ph↗

arXiv2004

Finsleroid space with angle and scalar product

A systematic approach has been developed to encompass the Minkowski-type extension of Euclidean geometry such that a one-vector anisotropy is permitted, retaining simultaneously the concept of angle. For the respective geometry, the Euclidean unit ball is to be replaced by the body which is convex and rotund and is found on assuming that its surface (the indicatrix extending the unit sphere) is a space of constant positive curvature. We have called the body the Finsleroid in view of its intrinsic relationship with the metric function of Finsler type. The main point of the present paper is the angle coming from geodesics through the cosine theorem, the underlying idea being to derive the angular measure from the solutions to the geodesic equation which prove to be obtainable in simple explicit forms. The substantive items concern geodesics, angle, scalar product, perpendicularity, and two-vector metric tensor. The Finsleroid-space-associated one-vector Finslerian metric function admits in quite a natural way an attractive two-vector extension.

math.MG↗

arXiv2003

Finsleroid-Space Supplemented by Angle

Our previous exploration of the $\cE_g^{PD}$-geometry has shown that the field is promising. Namely, the $\cE_g^{PD}$-approach is amenable to development of novel trends in relativistic and metric differential geometry and can particularly be effective in context of the Finslerian or Minkowskian Geometries. The main point of the present paper is the tenet that the $\cE_g^{PD}$-space-associated one-vector Finslerian metric function admits in quite a natural way an attractive two-vector extension, thereby giving rise to angle and scalar product. The underlying idea is to derive the angular measure from the solutions to the geodesic equation, which prove to be obtainable in an explicit simple form. The respective investigation is presented in Part I. Part II serves as an extended Addendum enclosing the material which is primary for the $\cE_g^{PD}$-space. The Finsleroid, instead of the unit sphere, is taken now as carrier proper of the spherical image. The indicatrix is, of course, our primary tool.

math-ph↗

arXiv2003

Finslerian Isospin--Nonlinear Equations for Pion and Spinor Interactions

The Finslerian curvature is introduced in the three-dimensional isospin space, suggesting that the isospin-pion field transforms according to non-linear Finslerian invariance transformations. The fundamental non-linear realization is associated with the pion field triplet. The Finslerian Lagrangian, as well as the implied pion-field selfinteraction, involves the first but no higher derivatives of the pion field. While the invariance transformations are now nonlinear, the conservation laws are still meaningful and sufficient to get the conservations for the energy-momentum and charges. The Finsler-invariant pion-nucleon Lagrangian function is also proposed. The Finslerian isospin-space symmetry is a pure interaction symmetry not shared by the asymptotic fields. The full Klein-Gordon-Dirac equation is accordingly extended. Various details of the implied Finsleroid-structure are formulated in an explicit way.

hep-ph↗

arXiv2002

Finslerian Post-Lorentzian Kinematic Transformations in Anisotropic-Space Case

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 space of constant negative curvature is still fulfilled. The method consists in evaluating respective Finslerian tetrads and then treating them as the bases of inertial reference frames. The Transport Synchronization has rigorously been proven, which opens up the ways proper to favour the concept of one-way light velocity. Transition to the Hamiltonian treatment is straightforward, so that the Finslerian transformation laws for momenta and frequences, as well as due Finslerian corrections to Doppler effect, become clear. An important common feature of the ordinary pseudo-Euclidean theory of special relativity and of the Finslerian relativistic approach under study is that they both endeavour to establish a universal prescription for applying the theory to systems in differing states of motion.

gr-qc↗

arXiv2002

Finslerian Extension of Lorentz Transformations and First-Order Censorship Theorem

Granted the post-Lorentzian relativistic kinematic transformations are described in the Finslerian framework, the uniformity between the actual light velocity anisotropy change and the anisotropic deformation of measuring rods can be the reason proper for the null results of the Michelson-Morley-type experiments at the first-order level.

gr-qc↗

arXiv2002

Finslerian Anisotropic Relativistic Metric Function Obtainable under Breakdown of Rotational Symmetry

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. By evaluating respective Finslerian tetrads, and treating them consistently as the bases of inertial reference frame (RF), the generalized Finslerian kinematic transformations follow in a convenient explicit form. The concomitant Finslerian relativistic relations generalize their Lorentzian prototypes through the presence of one characteristic parameter g, so that the constraints on the parameter may be found in future high-precision post-Lorentzian experiments. As the associated Finslerian Hamiltonian function is also obtainable in a clear explicit form, convenient prospects for the Finslerian extension of particle dynamics are also opened. Additionally, the Finslerian extension of the general-relativistic Schwarzschild metric can unambiguously be proposed.

gr-qc↗

arXiv2000

Finsleroids Reflect Future-Past Asymmetry of Space-Time

The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct violation of the $T-$parity, so that the future-past asymmetry of the physical world can stem from the $T-$asymmetry of the Finslerian indicatrix. Indeed the idea should compel much attention of physicists.

math-ph↗

arXiv2000

Can Neutrinos and High-Energy Particles Test Finsler Metric of Space-Time?

The Finsler-relativistic metric function $F(g;R)$ and the associated Hamiltonian function $H(g;P)$, being considered together with explicit Finslerian special-relativistic kinematic transformations, give rise to a self-consistent and rigorous framework upon which corrections to Lorentz-relativistic quantities can properly be evaluated. The concomitant relations generalize their Lorentzian prototypes through the presence of a single characteristic parameter, ~$g$, so that the explicated Particle-Antiparticle Asymmetry, as well as the search for possible distinction between the pseudo-Euclidean Light Geometry and the Finsler-relativistic Neutrino Geometry, can well be traced in terms of this parameter. At any fixed rest-mass value $m$ and $g\ne0$, the dependences of energy on three-dimensional momentum prove to be of different forms, as given by the respective functions $E^{(+)}(g;m;|{\bf P}|)$ and $E^{(-)}(g;m;|{\bf P}|)$, for particles and antiparticles. This splitting of the mass-shell, as well as various entailed Finslerian approximations with respect to $g$, can naturally be proposed for experimental study in order to obtain estimations on $g$. Since neutrinos and antineutrinos are uncomposed neat particles, measuring the difference between their velocities seems to be the best way for testing implied Finslerian corrections to conventional Lorentzian quantities. Accelerators which can produce neutrinos and antineutrinos are ideal instruments to gain this aim. The known measurements led to the conclusion that the difference $<0.7\cdot 10^{-4}~(95%~CL)$, while announced future long baseline neutrino experiments probably raise the sensitivity to approach the high level of $\sim 10^{-9}$.

hep-ph↗