Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
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1.4 Units• from now on, we will use units which will give us numbers with natural orderof magnitude for quantum mechanics and relativistic kinematics̷h = c = 1 . (17)• velocities and actions are dimensionless and therefore[ ]1[energy] = [momentum] = [mass] = . (18)length• in particular, our <strong>Feynman</strong> rules, will later yield cross sections in units of [energy −2 ],e. g.• the relevant conversion factors are(TeV 2 nb = GeV 2 mb) and therefore2 Asymptotic Statesσ = 4πα23E 2 (19)̷hc = 197.327 053(59) MeV fm (20)(̷hc) 2 = 0.389 379 66(23) TeV 2 nb (21)σ =• described by wave equations, that are4πα 23(E/TeV) 2 0.39 nb (19′ )1. linear: superposition principle of quantum mechanics2. relativistic: matrix elements of observables must transform under rotationsand Lorentz boosts like scalars, four vectors, tensors, &c.3. and have the correct dispersion relation: E 2 = ⃗p 2 + m 2• objects of interest– spin-0 particles: not yet unambigously observed as an elementary particle,but ATLAS and CMS have strong evidence for a state with spin 0 or 2∗ one invariant component– spin-1/2 particles: leptons, quarks∗ at least two components: spinor under rotations– spin-1 particles: gauge bosons∗ massive three components (polarizations)∗ massless two components (polarizations)4