89,307 research outputs found
Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity
Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. {\bf
107}, 181803 (2011)] pointed out that the superluminal neutrinos reported by
the OPERA would lose their energy rapidly via the Cherenkov-like process. The
Cherenkov-like process for the superluminal particles would be forbidden if the
principle of special relativity holds in any frame instead violated with a
preferred frame. We have proposed that the Finslerian special relativity could
account for the data of the neutrino superluminality (arXiv:1110.6673[hep-ph]).
The Finslerian special relativity preserves the principle of special relativity
and involves a preferred direction while consists with the causality. In this
paper, we prove that the energy-momentum conservation is preserved and the
energy-momentum is well defined in Finslerian special relativity. The
Cherenkov-like process is forbidden in the Finslerian special relativity. Thus,
the superluminal neutrinos would not lose energy in their distant propagation.Comment: 9 pages, no figure. Version for publication in PL
Cosmological model with local symmetry of very special relativity and constraints on it from supernovae
Based on Cohen \& Glashow's very special relativity [A. G. Cohen and S. L.
Glashow, Phys. Rev. Lett. {\bf 97} (2006) 021601], we propose an anisotropic
modification to the Friedmann-Robertson-Walker (FRW) line element. An
arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the
Randers-Finsler type. The 1-form picks out a privileged axis in the universe.
Thus, the cosmological redshift as well as the Hubble diagram of the type Ia
supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2
compilation, we obtain the privileged axis pointing to
(). This privileged axis is close to those obtained by
comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be
noticed that the result is consistent with isotropy at the level
since the anisotropic magnitude is .Comment: 13 pages, 2 figures. Published at EPJC(2013
Harnack inequalities and B\^ocher-type theorems for conformally invariant fully nonlinear degenerate elliptic equations
We give a generalization of a theorem of B\^ocher for the Laplace equation to
a class of conformally invariant fully nonlinear degenerate elliptic equations.
We also prove a Harnack inequality for locally Lipschitz viscosity solutions
and a classification of continuous radially symmetric viscosity solutions.Comment: to appear in CPA
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