P501B Advanced QFT
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:
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:
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:
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.
- 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:
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The course will assessed according to the following three components:
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.
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
- Action integrals and partition functions in quantum gravity , G. Gibbons and S. Hawking, Phys. Rev. D 15, 2752-2756 (1977)
- Path-integral derivation of black-hole radiance , J. Hartle and S. Hawking, Phys. Rev. D 13, 2188-2203 (1976)
Vacuum tunneling in field theory
- Gravitational effects on and of vacuum decay , S. Coleman and D. De Luccia, Phys. Rev. D 21, 3305 (1980)
Instanton effects in gauge theories
- Computation of the quantum effects due to a four-dimensional pseudoparticle , G. 't Hooft, Phys. Rev. D 14, 3432 (1976)
Lattice gauge theory
- Confinement of quarks , K. Wilson, Phys. Rev. D10, 2445 (1974)
Functional integrals in finite temperature field theory
- Feynman rules for gauge theories at finite temperature , C. Bernard, Phys. Rev. D9, 3312 (1974)
- Finite-temperature quantum field theory in Minkowski space , A. Niemi and G. Semenoff, Ann. Phys. 152, 105 (1984)
Radiative symmetry breaking
- Radiative Corrections as the Origin of Spontaneous Symmetry Breaking , S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973)
Wilsonian RG, critical phenomena, and the epsilon expansion
- The renormalization group and the epsilon expansion, K. Wilson and J. Kogut, Phys. Rep. 12, 75 (1974)
Chiral perturbation theory as an effective field theory in QCD
- Chiral perturbation theory to one loop , J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984)
Scale dependence (DGLAP evolution) of parton distributions in QCD
- Asymptotic freedom in parton language , G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977)
Resonances, correlation functions, and spectral (SVZ) sum rules in QCD
- QCD and resonance physics. applications , M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 147, 448 (1979)
- QCD and resonance physics. theoretical foundations , M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 147, 385 (1979)
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)
- Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory , A. Zamolodchikov, JETP Lett. 43, 730 (1986)
- c-theorem and spectral representation ,A. Capelli. D. Friedan and J. Latorre, Nucl. Phys. B 352, 616 (1991)
- On renormalization group flows in four dimensions , Z. Komargodksi and A. Schwimmer, JHEP 12, 99 (2011)
Gauge anomalies and chiral theories
- Gauge anomalies in an effective field theory , J. Preskill, Ann. Phys. (1991) 323
Gravitational Anomalies
- The gravitational correction to PCAC , R. Delbourgo, A. Salam, Phys.Lett. B40 (1972) 381
- Gravitational anomalies , L. Alvarez-Gaume, E. Witten, Nucl.Phys. B234 (1984) 269
Renormalization of Nonabelian Gauge Theories (*NB: more technical topic*)
- Renormalization of massless Yang-Mills fields , G. 't Hooft, Nucl.Phys. B33 (1971) 173
- Renormalizable lagrangians for massive Yang-Mills fields , G. 't Hooft, Nucl.Phys. B35 (1971) 167
- Renormalization of gauge theories - unbroken and broken , B. Lee, Phys. Rev. D 9, 933 (1974) [see also the references to Lee and Zinn-Zustin therein]