# 2: PoincarĂ© Transformations

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The basic equations of relativistic quantum mechanics, the Poincaré Algebra, are presented and discussed in Chapter 2 and derived in Chapter 4. In this chapter we set the stage for the derivation in Chapter 4 by discussing Poincaré transformations and defining what is meant by Lorentz invariance of a physical system. Poincaré transformations of preparation and measurement apparatuses are defined in Section 3.1, Lorentz invariance of a physical system is defined in Section 3.2, Poincaré transformations in Hilbert space are given in Section 3.3, three- and four-vector operators are discussed in Sections 3.4 and 3.5, Poincaré transformations of some operators are given in Section 3.6 and derivations of some results are given in Section 3.7.