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2.6 Systematic vs. non-systematic violations

Most tests of Lorentz violation deal with systematic Lorentz violation, where the deviation is constant in time/space. For example, consider the modified dispersion relation w2 = k2 + f (4)k4/E2Pl for a photon where f(4) is some fixed coefficient. There is no position dependence, so the Lorentz violating term is a constant as the particle propagates. However, various models [99Jump To The Next Citation Point255Jump To The Next Citation Point231Jump To The Next Citation Point] suggest that particle energy/momentum may not be constant but instead vary randomly by a small amount. Some authors have combined these two ideas about quantum gravity, Lorentz violation and stochastic fluctuations, and considered a stochastic violation of Lorentz invariance characterized by a fluctuating coefficient [12Jump To The Next Citation Point232Jump To The Next Citation Point24Jump To The Next Citation Point108115]. We will discuss non-systematic models in greater detail in Section 3.5.
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