2007/07/31 by G. W. Gibbons, Joaquim Gomis, C.N. Pope +1 · 2 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.76.081701
published as Phys.Rev.D76:081701,2007 · 4 pages, minor corrections, references added
arxiv created 2007/08/20 · openalex publication_date 2007/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We ask whether Cohen and Glashow's very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time 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 noncommutative translations analogous to those of the de Sitter deformation of the Poincar'e group: space-time remains flat. Only a 1-parameter family DISIMb(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 DISIMb(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIMb(2)-invariant wave equations for particles of spins 0, (1)/(2), and 1. The experimental bound, |b|<10^\ensuremath-26, raises the question ``Why is the dimensionless constant b so small in very special relativity?''