General Very Special Relativity is Finsler Geometry

@misc{citeulike:1460568, abstract = {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 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 Poincar\'e 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?''}, author = {Gibbons, G. W. and Gomis, Joaquim and Pope, C. N. }, citeulike-article-id = {1460568}, eprint = {0707.2174}, keywords = {cosmology}, month = {Jul}, posted-at = {2007-07-17 04:44:04}, priority = {2}, title = {General Very Special Relativity is Finsler Geometry}, url = {http://arxiv.org/abs/0707.2174}, year = {2007} }

TY - ELEC ID - citeulike:1460568 L3 - citeulike-article-id:1460568 N2 - 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 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 Poincar\'e 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?'' TI - General Very Special Relativity is Finsler Geometry KW - cosmology AU - Gibbons, GW AU - Gomis, Joaquim AU - Pope, CN PY - 2007/Jul/14/ UR - http://arxiv.org/abs/0707.2174 ER -