# Electromagnetic field in Finsler and associated spaces

01 Jul 2002-International Journal of Theoretical Physics (Kluwer Academic Publishers-Plenum Publishers)-Vol. 41, Iss: 7, pp 1307-1325

TL;DR: In this paper, the electromagnetic field and its interaction with the leptons are introduced in Finsler space and the field equations are derived from a property of the fields on the autoparallel curve.

Abstract: The electromagnetic field and its interaction with the leptons is introduced in Finsler space. This space is also considered as the microlocal space-time of the extended hadrons. The field equations for the Finsler space have been obtained from the classical field equations by quantum generalization of this space-time below a fundamental length-scale. On the other hand, the classical field equations are derived from a property of the fields on the autoparallel curve of the Finsler space. The field equations for the associated spaces of the Finsler space, which are macroscopic spaces, such as the large-scale space-time of the universe and the usual Minkowski space-time, can also be obtained for the case of Finslerian bispinor fields separable as the direct products of fields depending on the position coordinates with those depending on the directional arguments. The equations for the coordinate-dependent fields are the usual field equations with the cosmic time-dependent masses of the leptons. The other equations of the directional variable-dependent fields are solved here. Also, the lepton current and the continuity equation are considered. The form-invariance of the field equations under the general coordinate transformations of the Finsler spaces has been discussed.

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01 Mar 2015TL;DR: In this article, the authors assume that the strong interactions of baryons and mesons are correctly described in terms of the broken "eightfold way", and they are tempted to look for some fundamental explanation of the situation.

Abstract: If we assume that the strong interactions of baryons
and mesons are correctly described in terms of
the broken "eightfold way", we are tempted to
look for some fundamental explanation of the situation.
A highly promised approach is the purely dynamical
"bootstrap" model for all the strongly interacting
particles within which one may try to derive
isotopic spin and strangeness conservation and
broken eightfold symmetry from self-consistency
alone. Of course, with only strong interactions,
the orientation of the asymmetry in the unitary
space cannot be specified; one hopes that in some
way the selection of specific components of the F-spin
by electromagnetism and the weak interactions
determines the choice of isotopic spin and hypercharge
directions.

361 citations

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TL;DR: In this article, the authors assume that the strong interactions of baryons and mesons are correctly described in terms of the broken "eightfold way", and they are tempted to look for some fundamental explanation of the situation.

2,244 citations

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01 Jan 1972

TL;DR: Feynman as mentioned in this paper proposed the Parton Model and showed that it can be used to explain low-energy photon reactions at extreme energies and the properties of operators in momentum space.

Abstract: * Editors Foreword Richard P. Feynman * 15 General Theoretical Background * 68 Low Energy Photon Reactions * 810 Quark Model of Resonances * 1112 Pseudoscalar Meson Photoproduction, High Energy * 1314 t-Channel Exchange Phenomena * 1421 Vector Mesons and Vector Meson Dominance Hypothesis * 2224 Electromagnetic Form Factors * 2526 Electron-Proton Scattering. Deep Inelastic Region * 2633 Parton Model * 3435 Tests of the Parton Model * 3637 Inelastic Scattering As Properties of Operators * 38 Light Cone Algebra * 3941 Properties of Commutators in Momentum Space * 4247 Electromagnetic Self Energy * 4849 Other Two-Current Effects * 5051 Hypothesis in the Parton Model * 5254 Hadron-Hadron Collisions at Extreme Energies * 55 Final Hadronic States in Deep Inelastic Scattering * 5657 Partons as Quarks

1,394 citations

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TL;DR: In this paper, the authors show that the infinite-momentum limit for these commutators does not diverge, but may vanish, if the limit is nonvanishing.

Abstract: By combining the ${q}_{0}\ensuremath{\rightarrow}i\ensuremath{\infty}$ method for asymptotic sum rules with the $P\ensuremath{\rightarrow}\ensuremath{\infty}$ method of Fubini and Furlan, we relate the structure functions ${W}_{2}$ and ${W}_{1}$ in inelastic lepton-nucleon scattering to matrix elements of commutators of currents at almost equal times at infinite momentum. We argue that the infinite-momentum limit for these commutators does not diverge, but may vanish. If the limit is nonvanishing, we predict $\ensuremath{
u}{W}_{2}(\ensuremath{
u}, {q}^{2})\ensuremath{\rightarrow}{f}_{2}(\frac{\ensuremath{
u}}{{q}^{2}})$ and ${W}_{1}(\ensuremath{
u}, {q}^{2})\ensuremath{\rightarrow}{f}_{1}(\frac{\ensuremath{
u}}{{q}^{2}})$ as $\ensuremath{
u}$ and ${q}^{2}$ tend to $\ensuremath{\infty}$. From a similar analysis for neutrino processes, we conclude that at high energies the total neutrino-nucleon cross sections rise linearly with neutrino laboratory energy until nonlocality of the weak current-current coupling sets in. The sum of $\ensuremath{
u}p$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{
u}}p$ cross sections is determined by the equal-time commutator of the Cabibbo current with its time derivative, taken between proton states at infinite momentum.

829 citations

### "Electromagnetic field in Finsler an..." refers background in this paper

...In fact, the extended hadron-structure in such an anisotropic microscopic domain corresponds to the picture of composite character of hadrons, the origin of which lies in the works of Sakata (1956), Gell-Mann (1964), Bjorken (1969), and Feynman (1972)....

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TL;DR: Bell's theorem is demonstrated, without using inequalities, for an experiment with two particles, and it is shown that, if realism and Lorentz-invariant observables are assumed, it can derive a contradiction with quantum mechanics.

Abstract: First, we demonstrate Bell's theorem, without using inequalities, for an experiment with two particles. Then we show that, if we assume realism and we assume that the ``elements of reality'' corresponding to Lorentz-invariant observables are themselves Lorentz invariant, we can derive a contradiction with quantum mechanics.

669 citations