General very special relativity is Finsler geometry
- DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA (United Kingdom)
- Departament ECM, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)
- George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, Texas 77843-4242 (United States)
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 Poincare group: space-time remains flat. Only a 1-parameter family DISIM{sub 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{sub b}(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM{sub b}(2)-invariant wave equations for particles of spins 0, (1/2), and 1. The experimental bound, |b|<10{sup -26}, raises the question 'Why is the dimensionless constant b so small in very special relativity?'.
- OSTI ID:
- 21032408
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 76, Issue 8; Other Information: DOI: 10.1103/PhysRevD.76.081701; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Deforming the Maxwell-Sim algebra
An arena for model building in the Cohen-Glashow very special relativity