Effects of CPT and Lorentz Invariance Violation on Pulsar Kicks

The breakdown of Lorentz’s and CPT invariance, as described by the Extension of the Standard Model, gives rise to a modification of the dispersion relation of particles. Consequences of such a modification are reviewed in the framework of pulsar kicks induced by neutrino oscillations (active-sterile conversion). A peculiar feature of the modified energy-momentum relations is the occurrence of terms of the form $\delta \text{bbox}\mathrm{\Pi }\cdot \widehat{\mathbf{p}}$, where $\delta {\bbox \Pi}$ accounts for the difference of spatial components of flavor depending coefficients which lead to the departure of the Lorentz symmetry, and $\widehat{\mathbf{p}}=\mathbf{p}\mathrm{/}p$, being $\mathbf{p}$ the neutrino momentum. Owing to the relative orientation of $\mathbf{p}$ with respect to $\delta \text{bbox}\mathrm{\Pi }$, the {\it coupling} $\delta \text{bbox}\mathrm{\Pi }\cdot \widehat{\mathbf{p}}$ may induce the mechanism to generate the observed pulsar velocities. Topics related to the velocity distribution of pulsars are also discussed.