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Particles as Poincaré Representations
Particles as Poincaré Representations
foundations results +11 more phenomena owed owes (derived) definition 94.2: Symmetry transformation 94.2 Symmetry transfo… definition 94.15: Pauli–Lubanski vector 94.15 Pauli–Lubanski v… definition 94.19: Mass 94.19 Mass definition 94.23: Little group 94.23 Little group definition 94.34: Particle 94.34 Particle theorem 94.3: Wigner 94.3 Wigner corollary 94.4: Connected symmetry groups act unitarily 94.4 Connected symmet… theorem 94.5: Bargmann 94.5 Bargmann proposition 94.7: Composition law 94.7 Composition law proposition 94.8: The Poincaré algebra of the generators 94.8 The Poincaré alg… corollary 94.9: Rotations, boosts, translations 94.9 Rotations, boost… proposition 94.10: \SL(2,ℂ) covers the proper orthochronous
Lorentz group 94.10 \SL(2,ℂ) covers… lemma 94.11: Unitary elements give rotations 94.11 Unitary elements… lemma 94.12: Hermitian elements give boosts 94.12 Hermitian elemen… lemma 94.13: Boost–rotation decomposition 94.13 Boost–rotation d… corollary 94.14: SU(2) covers SO(3); half-integer spin is
projective 94.14 SU(2) covers SO(… lemma 94.16: Invariance identity for \epsilon 94.16 Invariance ident… lemma 94.17: Properties of \hatW 94.17 Properties of \h… phenomenon 94.30: Quantization of intrinsic angular momentum 94.30 Quantization of… pending : ch:03-poincare-representations@pending-1 pending pending : ch:03-poincare-representations@pending-2 pending The chain of Particles as Poincaré Representations: 21 of 32 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.