Anomalous Lorentz transformation and side jump of a massive fermion

The side jump in the anomalous Lorentz transformation, arising from the spin-orbit interactions, plays important roles in various intriguing physics, such as chiral vortical effects and spin polarization. In this work, the side jump of the spin-half massive particles, which has rarely been discussed, is visualized and evaluated for the first time. A compact analytical expression describing such side jumps is derived, and found approaching the one describing the chiral fermions in the massless limit. It is further demonstrated that the covariance of the total angular momentum, which would be broken by a normal Lorentz transformation, is restored after the obtained side jumps are taken into account.