  We show that electrons undergoing a two-particle collision in a crystal
experience a coordinate shift that depends on their single-particle Bloch wave
functions, and derive a gauge-invariant expression for such shift, valid for
arbitrary band structures, and arbitrary two-particle interaction potentials.
As an application of the theory, we consider two-particle coordinate shifts for
Weyl fermions in space of three spatial dimensions. We demonstrate that such
shifts in general contribute to the anomalous Hall conductivity of a clean
electron liquid.
