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Relativistic treatments of quantum mechanical systems are important forunderstanding hadronic structure and dynamics at sub-nucleon distance scales.Hadronic states in different inertial reference frames are needed to computecurrent matrix elements that probe hadronic structure and dynamics.Relativistic invariance is an important consideration as the resolution of theprobe is increased. Many different treatments of relativistic dynamics are usedin practice, including Poincar\'e covariant methods, Lorentz covariant methods,Euclidean covariant methods and methods based on quantum fields. Wave functionsare typically matrix elements of interacting relativistic states in a basis ofnon-interacting relativistic states. The purpose of this work is to develop therelation between these different representations of relativistic states thatare used in different applications from a unified point of view, starting withpositive mass irreducible representations of the Poincar\'e group.

physical review. c

Representations of relativistic particles of arbitrary spin in  Poincar\'e, Lorentz, and Euclidean covariant formulations of relativistic  quantum mechanics