We present a general description of the propagation properties of quantum gravity modified electrodynamics characterized by constitutive relations up to second order in the correction parameter. The effective description corresponds to an electrodynamics in a dispersive and absorptive non-local medium, where the Green functions and the refraction indices can be explicitly calculated. The reality of the electromagnetic field together with the requirement of causal propagation in a given referrence frame leads to restrictions in the form of such refraction indices. In particular, absorption must be present in all cases and, contrary to the usual assumption, it is the dominant aspect in those effective models which exhibit linear effects in the correction parameter not related to birefringence. In such a situation absorption is linear while propagation is quadratical in the correction parameter.
After summarizing the most interesting results in the calculation of synchrotron radiation in the Myers-Pospelov effective model for Lorentz invariance violating (LIV) electrodynamics, we present a general unified way of describing the radiation regime of LIV electrodynamics which include the following three different models : Gambini-Pullin, Ellis et al. and Myers-Pospelov. Such unification reduces to the standard approach of radiation in a dispersive and absortive (in general) medium with a given index of refraction. The formulation is presented up to second order in the LIV parameter and it is explicitly applied to the synchrotron radiation case.
We present an alternative method for constructing a consistent perturbative low energy canonical formalism for higher order time-derivative theories, which consists in appliying the standard Dirac method to the first order version of the higher order Lagrangian, augmented by additional perturbative Hamiltonian constraints. The method is purely algebraic, provides the dynamical formulation directly in phase space and can be used in singular theories without the need of initially fixing the gauge. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field with self-interaction. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory, after incorporating the projection to the space of physical modes. This comparison highligths the soundness of the present formalism.
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