Effective Field Theories
Course 0000002052 in WS 2014/5
|Semester Weekly Hours||4 SWS|
|Organisational Unit||Applied Quantum Field Theory|
Courses are together with exams the building blocks for modules. Please keep in mind that information on the contents, learning outcomes and, especially examination conditions are given on the module level only – see section "Assignment to Modules" above.
|additional remarks||The lecture course will provide an introduction to effective field theories (EFTs) and renormalization techniques with applications ranging from high energy to atomic physics. The following topics will be covered: * Principles of EFTs o Scales and systems in nature o What is an EFT and how to construct it o Example: the Euler-Heisenberg Lagrangian o Example: the Fermi theory of weak interactions at tree level o Example: the Rayleigh scattering o Relevant, irrelevant and marginal operators o Quantum loops of irrelevant operators o Mass-dependent vs mass-independent regularization schemes o Dimensional regularization o Quantum loops of marginal operators o Example: β function and running coupling constant in QED and QCD o Decoupling theorem o Example: the one and two loop matching of the QCD strong-coupling constant in MSbar o Renormalization group equations in QFTs and EFTs o Anomalous dimensions o Mixing o Example: ΔS = 2 transition amplitude in the Fermi theory of weak interactions * Heavy quark effective theory o Heavy-light meson spectrum o Heavy-quark spin-flavour symmetry o Static Lagrangian o Spectroscopy implications o Heavy meson decay constants o Transition form factors: Isgur-Wise functions o Example: B → D transitions and calculation of dΓ(B → D e ν)/dq² o Renormalization of composite operators o Example: heavy-light currents and heavy-heavy currents o Heavy meson decay constants at LL and NLO o The 1/m expansion of the HQET Lagrangian o Reparameterization invariance o Chromomagnetic coupling and hyperfine splitting at LL o Decoupling in the HQET o B → D e ν and Luke's theorem * Applications to atomic physics o Bound states in QED: physical picture, scales, degrees of freedom o NRQED: Lagrangian, power counting, matching o Four-fermion operators o Example: matching of dimension six four-fermion operators and the positronium decay width o pNRQED: Lagrangian, power counting, matching o Example: the hydrogen atom and the Lamb shift o Example: the Rayleigh scattering in pNRQED|