Lorentz-violating dispersion relations and threshold analyses
  Remnant low-energy effects of Planck-scale Lorentz breaking in candidate fundamental theories typically include modified one-particle dispersion relations. Theoretical constraints on such modifications are discussed leading to the exclusion of a variety of previously considered Lorentz-violating parameters. In particular, the fundamental principle of coordinate independence, the role of an effective dynamical framework, and the conditions of positivity and causality are investigated. 
Ralf Lehnert