Supersymmetry

Supersymmetry Herbi K. Dreiner Howard E. Haber September 22, 2004 Stephen P. Martin Contents Part 1: Fermions in Quantum Field Theory and the Standard Model 7 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Two-component formalism for Spin-1/2 Fermions The Lorentz group and its Lie algebra The Poincar´e group and its Lie algebra Spin-1/2 representation of the Lorentz group Bilinear covariants of two-component spinors Lagrangians for free spin-1/2 fermions The fermion mass-matrix and its diagonalization Discrete spacetime and internal symmetries Parity transformation of two-component spinors Time-reversal transformation of two-component spinors Charge conjugation of two-component spinors CP and CPT conjugation of two-component spinors 9 9 12 14 17 23 26 29 32 36 40 41 References 48 Feynman Rules for Fermions Fermion creation and annihilation operators Properties of the two-component spinor wave functions Charged two-component fermion fields Feynman rules for external two-component fermion lines Feynman rules for two-component fermion propagators Feynman rules for two-component fermion interactions General structure and rules for Feynman graphs Simple examples of Feynman diagrams and amplitudes 2.8.1 Tree-level decays 2.8.2 Tree-level scattering processes 49 49 50 54 56 57 61 65 67 67 69 2 Contents 3 2.9 Conventions for fermion and anti-fermion names and fields 76 3 3.1 3.2 3.3 3.4 3.5 From Two-Component to Four-Component Spinors Four-component spinors Lagrangians for free four-component fermions Properties of the four-component spinor wave functions Feynman rules for four-component Majorana fermions Simple examples of Feynman diagrams revisited 83 84 91 92 94 99 References