A discussion on Lorentz preserving scalar fields in Lorentz violating theory

Abstract

Abstract. Lorentz symmetry can be preserved in effective higher derivative scalar field theories containing a constant vector that breaks Lorentz invariance of flat spacetime, through the choice of special field configurations. These fields do satisfy the equations of motion, yielding cubic dispersion relations analogous to those derived earlier. Moreover, the Lie algebra of the Lorentz group can be realised on these fields. IntroductionPhysicists have focussed a lot of their attention on theoretically and experimentally probing departures from Lorentz symmetry for the better part of the last couple of decades, [1,2,3,4,5,6,7,8,9]. This search was initiated by different theories of quantum gravity that hypothesise violation of Lorentz symmetry in flat spacetime at energies E M P l , where M P l denotes the Planck mass. Deviations, suppressed by the Planck mass, from the standard special relativistic dispersion relation of free particles of mass m at high energies E (M P l E m) are considered to be signatures of quantum gravity induced Lorentz violation. Myers and Pospelov [6] constructed low energy effective actions of fields having spins 0, 1/2 and 1 that include new Planck suppressed dimension five operators, to account for these proposed corrections to the dispersion relations. In this report, we shall restrict ourselves to the case of a complex scalar field φ. The extended action of [6] is,