  We study the structure of maps that Lorentz boosts induce on the spin degree
of freedom of a system consisting of two massive spin-$1/2$ particles. We
consider the case where the spin state is described by the Werner state and the
momenta are discrete. Transformations on the spins are systematically
investigated in various boost scenarios by calculating the orbit and
concurrence of the bipartite spin state with different kinds of product and
entangled momenta. We confirm the general conclusion that Lorentz boosts cause
non-trivial behavior of bipartite spin entanglement. Visualization of the
evolution of the spin state is shown to be valuable in explaining the pattern
of concurrence. The idealized model provides a basis of explanation in terms of
which phenomena in systems involving continuous momenta can be understood.
