Very Special Relativity and TGD

One might think that Poincare symmetry is something thoroughly understood but the Very Special Relativity [1] proposed by nobelist Sheldon Glashow and Andrew Cohen suggests that this might belief might be wrong. Glashow and Cohen propose that instead of Poincare group, call it P , some subgroup of P might be physically more relevant than the whole P . To not lose four-momentum one must assume that this group is obtained as a semidirect product of some subgroup of Lorentz group with translations. The smallest subgroup, call it L2, is a 2-dimensional Abelian group generated by Kx + Jy and Ky − Jx. Here K refers to Lorentz boosts and J to rotations. This group leaves invariant light-like momentum in z direction. By adding Jz acting in L2 like rotations in plane, one obtains L3, the maximal subgroup leaving invariant light-like momentum in z direction. By adding also Kz one obtains the scalings of light-like momentum or equivalently, the isotropy group L4 of a light-like ray. The reasons why Glashow and Cohen regard these groups so interesting are following. a) All kinematical tests of Lorentz invariance are consistent with the reduction of Lorentz invariance to these symmetries. a) The representations of group L3 are one-dimensional in both massive and massless case (the latter is familiar from massless representations of Poincare group where particle states are characterized by helicity). The mass is invariant only under the smaller group. This might allow to have lefthanded massive neutrinos as well as massive fermions with spin dependent mass.