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3: More About the Poincaré Algebra

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  • We give a further discussion of the Poincaré Algebra (2.1) to (2.9) in this chapter. The derivation of the Poincaré Algebra is discussed in Section 4.1 and the Poincaré Algebra is written in a manifestly covariant form in Section 4.2. Lorentz invariants, operators invariant under all Poincaré transformations, are constructed in Section 4.3. Section 4.4 contains some matrix representations of the Lorentz Algebra, which is that part of the Poincaré Algebra corresponding to homogeneous Poincaré transformations (rotations and boosts). Also included is a demonstration of the relationship between 7-matrices and Lorentz boosts and a 4x4 matrix representation of the Poincaré generators. Finally, some derivations are given in Section 4.5.

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