Instructor:

E.S. Swanson
217 Allen Hall
4-9057       swansone@pitt.edu     http://fafnir.phyast.pitt.edu/py3765/

class meets Tuesday and Thursdays, 9:30-10:45, 105 Allen Hall.

Office Hours: Tuesday and Thursday, 11:00 - 12:00.

Introductory Texts:

(*) = required, (+) = strongly recommended

• (*) F. Mandl and G. Shaw, Quantum Field Theory
• F. Gross, Relativistic Quantum Mechanics and Field Theory

Reference Texts:

• (+) Donoghue, Golowich, and Holstein, Dynamics of the Standard Model
• (*) Peskin and Schroeder, An Introduction to Quantum Field Theory
• Itzykson and Zuber, Quantum Field Theory

Marking Scheme:   final = 0.4 take home exam + 0.6 assignments OR 1.0 assignments ...

Prerequisites:

You should be adept at quantum mechanics. Exposure to high energy physics, nuclear physics, tensors, relativistic EM, classical field theory, and quantum many-body physics would be very helpful but is not required. Taking the nuclear and high energy physics course is strongly recommended.

Assignments:

• asst1: EM Fields and Ladder Operators due Sept 4.

Syllabus QFT-I:

• Introduction to Second Quantization
  • Why Quantum Field Theory?
  • Second Quantization of the photon field
  • matter and light: nonrelativistic electrons, protons, and photons. Fermi's Goldon Rule, gauge invariance, black body radiation, Kramers-Heisenberg formula, Compton scattering, Rayleigh scattering, Thomson scattering, Coulomb gauge, photoelectric effect
  • first glimpse of renormalisation: the Lamb shift a la Bethe
• Spin-0 Fields
  • Klein-Gordon: propagators, causality, Feynman prescription, Noether's theorem, spectral function, energy-momentum tensor
  • interaction picture, S-matrix, Gell-Mann--Low theorem, Wick's theorem, Feynman rules, connected diagrams, scattering theory, decays, Mandlestam variables
  • another glimpse of renormalisation (tadpole diagrams)
• Spin-1/2 Fields
  • Dirac: spin statistic theorem, Lorentz invariance, bilinear currents, discrete symmetries, Diracology, trace theorems, helicity, chirality, the Foldy-Wouthuysen transformation
  • quantising: anticommutators, fermion propagator, chiral invariance, Feynman rules, the NJL model, fermion-scalar interactions, nonrelativistic interactions, nuclear physics (pi-N-N interaction)
• Spin-1 Fields
  • Electromagnetism: relativistic formalism, gauge fixing, Gupta-Bleuler presciption, Feynman prescription
  • quantising: photon propagator, Ward-Takahashi identities, infrared divergences, Feynman rules, P and C invariance, Yang's theorem, Furry's theorem
  • applications: Moeller scattering, Bhaba scattering, Klein-Nishina formula, decays, positronium decay, crossing symmetry, decay constants, B decays
• Renormalization I
  • fractals
  • an example from quantum mechanics: scattering via a delta-function
  • phi⁴ at one loop order: divergent diagrams, regularization, renormalization schemes, renormalization group, running coupling, fixed points and the beta function, Wick rotation, dimensional regularization, lambda(MS)/lambda(MS-bar)