The field theories construction in spacetime with deformed Poincaré subgroups symmetries

Abstract

The modern experiments have put strict restrictions on the possible violation of local Lorentz and CPT invariance. However there seem to exist some clues showing that the two symmetries are possibly broken. It would be remarkable to find out the possible breaking mechanism and build up a reasonable framework with Lorentz or CPT violation. As the spacetime corresponding to all possible of deformation of all the Poincare subgroups of the forms of semi product of the Lorentz subgroup with the spacetime translation are almost of Finsler type. We study here the particle dynamics in these Finsler spacetime and investigate their dispersion relations based on which we investigate the possible self-consistent field theories dynamics in the Finsler spacetime including scalar field, spinor field, vector field and gauge coupling. The modifications caused by deformation relative to field theories in Minkowski spacetime are discussed. The Finsler structures we study in this paper have strong dependence on the space-time direction. Thus, if space-time is of Finsler type, we can observe the dependence by well designed experiment.