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We study the structure of maps that Lorentz boosts induce on the spin degreeof freedom of a system consisting of two massive spin-$1/2$ particles. Weconsider the case where the spin state is described by the Werner state and themomenta are discrete. Transformations on the spins are systematicallyinvestigated in various boost scenarios by calculating the orbit andconcurrence of the bipartite spin state with different kinds of product andentangled momenta. We confirm the general conclusion that Lorentz boosts causenon-trivial behavior of bipartite spin entanglement. Visualization of theevolution of the spin state is shown to be valuable in explaining the patternof concurrence. The idealized model provides a basis of explanation in terms ofwhich phenomena in systems involving continuous momenta can be understood.

Entanglement of two relativistic particles with discrete momenta