Download Syllabus : Advanced Quantum Mechanics (Prof

Advanced Quantum Mechanics (III) (Prof. Schaden)
Course number 26.755.780. (Current Topics of Applied Physics, 3 credits)
Text: Advanced Quantum Mechanics by J.J. Sakurai (Addison-Wesley ISBN 0-201-06710-2)
Supplements:
Introduction to Quantum Field Theory by S.J. Chang (World Scientific ISBN 9971506815)
Quantum Field Theory (Revised Edition) by F. Mandl and G. Shaw (Wiley ISBN 0-471-94186-7)
This graduate level course is an introduction to quantum field theory using canonical quantization.
The emphasis is on the application of field theoretic concepts and methods to understand and be
able to calculate such diverse effects as: spontaneous emission and decay rates, scattering crosssections (including their polarization dependence), relativistic corrections, the Lamb shift and
Casimir- as well as medium- effects. Familiarity with non-relativistic quantum mechanics and
classical electrodynamics is assumed but no prior knowledge of relativistic quantum mechanics or
quantum field theory is required. The S-matrix is introduced fairly early and tree-level crosssections are calculated using time-dependent perturbation theory. We will cover Dirac’s covariant
description of electrons and positrons together and their canonical quantization -- with nonrelativistic approximations being derived. An explicitly covariant description of the S-matrix in
terms of Feynman’s diagrams is presented in the latter part of the course and is used to give a short
introduction to mass and charge renormalization.
Below is a rough and preliminary time-table of the topics that will be covered. Weekly homework
assignments will be graded and discussed. Since this course is not a requirement, your personal
interest and active participation are taken for granted.
1st & 2nd wk: Classical field theory:
-- Lagrangian and Hamiltonian equations of motion and Poisson brackets.
-- Symmetries and Noether currents:
-- Translation symmetries and Energy & Momentum
-- Lorentz symmetry and Spin
-- Internal symmetries, minimal coupling and charges
3rd & 4th wk: Canonical quantization of free fields:
-- creation & annihilation operators and the number basis
-- quantization of a string subject to harmonic forces
-- of a free (charged) scalar field
-- Fermi-statistics and the quantization of non-interacting fermions
4th & 5th wk: Canonical quantization of the radiation field:
-- Maxwell’s equations in transverse (Coulomb) gauge
-- quantization of the transverse radiation field
-- emission and absorption of photons by atoms
-- Kramers-Heisenberg formula for photon scattering (tree-level)
Raileigh- & Thomson- scattering and the Raman effect
-- radiation damping and resonance fluorescence
-- Causality and the analyticity of the forward scattering amplitude
-- Self-energies: Casimir energy and Lamb shift (Bethe’s estimate)
6th & 7th wk: Dirac’s field equation describing relativistic spin ½ particles:
-- relativistic generalization of the Schrödinger equation
-- the electron spin magnetic moment and Dirac’s equation and Hamiltonian
-- Conserved currents and covariant bilinears
-- Relativistic covariance and C, P & T transformations
-- Effective Hamiltonian NR-approximation: Thomas & Darwin terms
-- Exact solutions: plane waves and the H-atom
-- quantization of the Dirac field and a little bit of hole theory.
-- interactions and positive & negative frequency components
-- weak interactions and parity (non-)conservation
8th & 9th wk: Covariant perturbation theory:
-- unitarity of S-matrix expansion in the interaction representation
-- (Covariant) first order processes: decay rates (and Mott scattering)
-- Second and higher order processes: time-ordered graphs
-- Wick time-ordered product and the electron propagator
-- Feynman’s space-time approach to electron and photon propagators
-- Introduction to Feynman diagrams
-two-photon annihilation
-Møller scattering
10th wk:
Selected topics:
Introduction to renormalization:
-- Mass and charge renormalization; the Lamb Shift revisited
OR The Electron Gas Model OR Zero Temperature Interacting Bose System
-- Hartree Fock Approximation and Self-energies
-- Effects:Decay of Electrons and Holes OR Interaction with the condensate