  The Thomas--Wigner rotation (TWR) results from the fact that a combination of
boosts leads to a non-trivial rotation of a physical system. Its origin lies in
the structure of the Lorentz group. In this article we discuss the idea that
the TWR can be understood in the geometric manner, being caused by the
non-trivially curved relativistic momentum space, i.e. the mass shell, seen as
a Riemannian manifold. We show explicitly how the TWR for a massive spin-$1/2$
particle can be calculated as a holonomy of the mass shell. To reach this
conclusion we recall how to construct the spin bundle over the mass shell
manifold.
