Lorentz violation at high energy: concepts, phenomena and astrophysical constraints

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the effective field theory approach to describing LV, the issue of naturalness, and many phenomena characteristic of LV. We discuss some of the current observational bounds on LV, focusing mostly on those from high energy astrophysics in the QED sector at order E/M_Planck. In this context we present a number of new results which include the explicit computation of rates of the most relevant LV processes, the derivation of a new photon decay constraint, and modification of previous constraints taking proper account of the helicity dependence of the LV parameters implied by effective field theory.