Lorentz Invariance Violation: Modification of the Compton Scattering and the GZK Cutoff and Other Effects

High Energy Effects of Noncommutative Spacetime Geometry

“…neglecting the higher order terms consisting α. This result also helped in explaining the GZK cutoff and the Lamb shift phenomenon in two previous papers [27,28]. Essentially, |λ| ≈ α 2π , is the reduced fine structure constant.…”

“…Apparently, there is a shift from the known values of the energy levels which should be observed in experiments. This fact can be correlated to the modified mass-energy relation that has been studied in our previous works [26,27]. For a general case, we can write…”

“…Now, from equation (27) we can infer three possible cases (with λ = −10 −3 ), as follows 1) For, p = mc we would have…”

Perturbative calculation of energy levels for the Dirac equation with generalised momenta

“…For this purpose, we may use certain types of astrophysical phenomena in which we can detect individual variations in their energy or in their observation time that are natural consequences of the theory. Indeed, there are indications that this type of situations may be present in phenomena such as the GZK cut-off where variations of the relationship between energy and momenta exist [1], or a generalised uncertainty principle comes into play [2]. This class of phenomena will also help to infer if specific features of some theory of quantum gravity are having a non-trivial influence at low energies as pointed out in [3].…”

“…The introduction of a minimum length scale is a structural feature within some theories of quantum gravity [4,5,6]. The existence of a minimum length is intimately related to generalised uncertainty principles [2,7] or as a consequence of a modified energy-momentum dispersion relation [8,1]. The concept of generalised momenta incorporates into a theory, a minimum length in a straightforward way and hence, quantum gravity effects up to a certain extent.…”