General Very Special Relativity is Finsler Geometry

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dc.creatorGibbons, G. W.
dc.creatorGomis, Joaquim
dc.creatorPope, C. N.
dc.date2007-07-14
dc.date2007-08-20
dc.date.accessioned2026-07-07T11:17:48Z
dc.date.available2026-07-07T11:17:48Z
dc.descriptionWe ask whether Cohen and Glashow's Very Special Relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved spacetime with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to non-commutative translations analogous to those of the de Sitter deformation of the Poincaré group: spacetime remains flat. Only a 1-parameter family DISIM_b(2) of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point particle action invariant under DISIM_b(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM_b(2)-invariant wave equations for particles of spins 0, 1/2 and 1. The experimental bound, $|b|<10^{-26}$, raises the question ``Why is the dimensionless constant $b$ so small in Very Special Relativity?''
dc.description4 pages, minor corrections, references added
dc.identifierhttps://arxiv.org/abs/0707.2174
dc.identifierhttp://arxiv.org/abs/0707.2174
dc.identifierPhys.Rev.D76:081701,2007
dc.identifierdoi:10.1103/PhysRevD.76.081701
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193131
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Phenomenology
dc.titleGeneral Very Special Relativity is Finsler Geometry
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