Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012
365 Thackeray Hall
4-9057 firstname.lastname@example.org http://fafnir.phyast.pitt.edu/py3765/
class meets Tuesday and Thursdays, 2:30-3:45, 316 OEH
Office Hours: Tuesday and Thursday, 3:45 - 4:45.
(*) = required, (+) = strongly recommended
- F. Mandl and G. Shaw, Quantum Field Theory
- (*) Peskin and Schroeder, An Introduction to Quantum Field Theory
- F. Gross, Relativistic Quantum Mechanics and Field Theory
- (+) Donoghue, Golowich, and Holstein, Dynamics of the Standard Model
- Itzykson and Zuber, Quantum Field Theory
Marking Scheme: final = 0.4 take home exam + 0.6 assignments OR 1.0 assignments ...
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.
We will be covering essentially all of Peskin and Schroeder over the two terms of this course. This text, like most other QFT texts, concentrates on teaching the methods of quantum field theory. There are precious few applications. Thus it is important that you take Nuclear and Particle Physics. Donoghue et al. is also a wonderful resource with many applications and advanced topics. I will supplement the material of Peskin and Schroeder with
- historical introduction
- the particle+wave picture
- the Lamb shift
- renormalising phi4 theory, the running coupling, relating different renormalisation schemes
- issues with the path integral
- Schwinger-Dyson equations
- Bethe-Salpeter equation
- Young tablueaux
- the strong CP problem
- effective field theory
- problems with the Standard Model
An important technical point: Peskin and Schroeder introduce the Dim Reg renormalization in an ad-hoc way, we will follow the traditional approach of introducing the scale via the coupling.
We will also use a simpler and more direct method to obtain the beta function than is used in the text.
Time constraints will force us to cover many of these topics superficially. Quantum field theory is an enormous topic; this course only gets you started. There is no second course, so you must read, read, read to learn more. I have assembled the following files to help you in this regard.
Quantum Field Theory Texts
Newer Important Articles
- Dyson QFT Freeman Dyson's classic QFT notes from Cornell, 1951
- Coleman QFT Sidney Coleman's QFT notes from Harvard, 1985
- 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,
- 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
- 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
- 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)