P501B Advanced QFT

Instructor: Adam Ritz
Office: Elliott 103
Email: aritz@uvic.ca

This is a one semester graduate course on aspects of quantum field theory, with a focus on the modern language of (Wilsonian) effective field theory. The course will have three main components: 

  • Path integral methods
  • Renormalization
  • Applications

See the course syllabus for further details.

Preparation: A working knowledge of canonical QFT as covered in PHYS 501A is assumed, along with upper level quantum mechanics and classical field theory (particularly electrodynamics), as covered in P502A Classical Electrodynamics and P500A Quantum Mechanics. Knowledge of nonabelian gauge theories, as covered in PHYS 509 would also be useful, but not essential.

This is a one semester graduate course on aspects of quantum field theory, with a focus on the modern language of (Wilsonian) effective field theory. The course will have three main components:
  • Path Integral Methods
    • path integrals in QM & field theory
    • propagators & correlation function
    • Dirac fields, gauge fields and ghosts
    • the perturbation expansion
    • symmetries, Ward identities
  • Renormalization
    • UV divergences, cutoff dependence
    • Wilsonian picture, renormalization group
    • classification of divergences, renormalized perturbation theory
    • Callan-Symanzik equation, running couplings
  • Applications
    • 1. Beta function in QCD
    • 2. QED and the photon effective action
The optional (but recommended) text for the course is:
  • An Introduction to Quantum Field Theory, M.E. Peskin and D.V. Schroeder

This has become the standard QFT textbook, providing an up-to-date and comprehensive tour through the subject. This course will broadly follow the second third (part II) of this book, with some variations and possibly some additions from part III and elsewhere. Although we wont cover them, one of the primary aims of the course will be to provide a solid coverage of techniques that should allow the later chapters on other aspects of the Standard Model of particle physics to be quite accessible.

Another recently published and useful text is:
  • Quantum Field Theory, M. Srednicki

This book takes a slightly different approach to Peskin & Schroeder, but covers similar ground and may provide a useful pedagogical alternative. It is structured with short lecture-style chapters, and is particularly useful in filling in a number of the calculational details.

Another significant text is:
  • The Quantum Theory of Fields, I and II , S. Weinberg

By one the trio annointed with the Nobel Prize for the Standard Model (with Glashow and Salam), this is already an important reference text. It contains a lot of insight and can be very useful for understanding some of the more subtle details skipped over elsewhere.

This is just a short list, and there are many other good QFT texts, a number of which are available in the library. You will also find many useful QFT reviews and lecture notes online.
Further online material for the course will be provided, including:

  • course notes
  • assignment sheets
  • sample solutions
The course will assessed according to the following three components:

  • Assignments: 50%
  • Project: 25%
  • Presentation: 25%

There will be a few assignments during the semester. The final assessment component will be an individual project, requiring some background research and a written report of approximately 15 pages, and a presentation. Possible projects are outlined under the relevant tab. 

The final grade follows the University's universal conversion between letter and percentage grades:

  • A+  (90-100)
  • A    (85-89)
  • A-   (80-84)
  • B+  (77-79)
  • B    (73-76)
  • B-   (70-72)
  • C+  (65-69)
  • C    (60-64)
  • D    (50-59)
  • F    (0-49)

If the application of this scheme would result in grades deemed by the instructor to be inconsistent with the University's grading descriptions (to be found on p.38 of the current Undergraduate Calendar), percentages will be assigned which are consistent with them.

NB: Use of calculators in exams

On all examinations the only acceptable calculator is the Sharp EL-510R. This calculator can be bought in the Bookstore for about $10. DO NOT bring any other calculator to the examinations.
The final assignment for the course will be an individual project focussing on a particular process or calculation in QFT. The suggestions below build on the topics disucssed in the early lectures (path integrals, renormalization, effective theories). They're based on one or more well-known papers, and understanding and describing some of those results can form the basis of your project. You should feel free to focus on specific aspects, and moreover you're welcome (and indeed encouraged) to read further and explore different directions of interest. Other choices of topic are of course welcome - you should view this as an opporunity to learn about a topic of interest in QFT that goes beyond the material covered in the lectures. Just come and talk to me to get the topic approved.

Assessment will be via a 25+5 minute presentation to the class, and an associated written report (the size is up to you, but it is expected that a full description would require at least 10 pages). You should try to prepare your seminar carefully so that it covers the basic physical picture, some of the relevant calculational details, and that you focus on what you found to be the most important or interesting aspects.

Here are some helpful guidelines on preparing and presenting talks.

Gravity and Path integrals

Vacuum tunneling in field theory

Instanton effects in gauge theories

Lattice gauge theory

Functional integrals in finite temperature field theory

Radiative symmetry breaking

Wilsonian RG, critical phenomena, and the epsilon expansion

Chiral perturbation theory as an effective field theory in QCD

Scale dependence (DGLAP evolution) of parton distributions in QCD

Resonances, correlation functions, and spectral (SVZ) sum rules in QCD

Effective field theory (and phenomenology) of extra dimensions

  • Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity , N. Arkani-Hamed, S. Dimopoulos, G. Dvali, Phys.Rev. D59 (1999) 086004

Constraints on RG flows (c-theorem)

Gauge anomalies and chiral theories

Gravitational Anomalies

Renormalization of Nonabelian Gauge Theories (*NB: more technical topic*)