PHY 611

                                                        Quantum Field Theory II

                                                                                Lecturer: Leonardo Rastelli 



Welcome to the home page of QFT II for Fall 2017.  Quantum field theory is the mathematical framework of all of particle physics and the indispensable language of a large body of statistical mechanics and of quantum many body physics. It is an incredibly rich subject that you will keep learning for the rest of your scientific life.

Learning QFT is qualitatively different from learning other advanced subjects, such as quantum mechanics and classical general relativity, which have a more established logical framework, and have been formalized even to the satisfaction of mathematicians. QFT is still an open subject, close to the conceptual frontier of theoretical physics. It is a work in progress, enriched by new viewpoints, simplified and extended in unexpected directions by each generation of theorists.

This is the second semester of a two-semester sequence. The material of QFTI (PHY610) will be assumed as prerequisite. First year graduate students who have taken QFT elsewhere may be able to take this class, depending on their level of preparation. You can get a detailed picture of what was covered by browsing the webpage of PHY610 for Spring 2017,

Course Outline:  We will start by reviewing and deepening our understanding of the Wilsonian viewpoint on QFT - notably the connection between renormalization and critical phenomena - which we quickly introduced at the end of last semester. We will then move on to new topics:  Abelian and non-abelian gauge theories and their path-integral quantization. One-loop calculations in quantum electrodynamics and Yang-Mills theory.  Asymptotic freedom of non-abelian gauge theories. Anomalies. Spontaneous symmetry breaking of global symmetries. Chiral Lagrangians (example of pion physics).  Spontaneous symmetry breaking of gauge symmetries.  Phases of gauge theories.  Introduction to the Standard Model of particle physics.


I plan to mostly use parts of Srednicki, Weinberg vol II, and Peskin&Schroeder. For the first few lectures on the Wilsonian RG, Cardy's book is a good reference.  Other material  and notes will be used for special topics.

M. Srednicki, Quantum Field Theory, Cambridge University Press.
Very clear short chapters. Particularly strong on technical details and explicit calculations.
A draft of the book is available on the author's webpage.

S. Weinberg, The Quantum theory of Fields, Cambridge University Press. Three volumes.
By one of the masters of the subject. Not an easy read but definitely worth it.
Volume I provides a compelling case that the formalism of quantum field theory inevitably arises from the marriage of special relativity and quantum mechanics. Probably best to read after you have mastered the basics of QFT. Volume II has some of the best treatments of several advanced topics (unsurpassed is the treatment of symmetry breaking, for example). Ditto for Volume III (on supersymmetry).  Cumbersome notation throughout -- the use of four-component spinors in volume three is infuriating.

J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press.
A gem. Very physical treatment of renormalization in the context of statistical mechanics.

Other textbooks:

To get oriented in a difficult subject that will likely challenge you both conceptually and technically, I very strongly recommend reading Zee's book:
A. Zee, Quantum Field Theory in a Nutshell, Princeton University Press
Zee gets to the core ideas keeping the technicalities to a minimum and is fun to read. Perfect for bedtime reading. We won't it use it as the main textbook because we'll need to develop the calculational machinery in greater depth.

M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press.
Recent textbook, building up to a comprehensive treatment of the Standard Model.

M. Peskin and D. Schroder, An introduction to quantum field theory, Addison-Wesley.
P&S has been the standard textbook for several years, and still has a lot of useful material. Chapter 5 (scattering process in QED) and Part II (an attempt to bridge the gap between the diagrammatic and Wilsonian viewpoints on renormalization theory) are particularly recommended.

T. Banks, Modern Quantum Field Theory: A concise introduction, Cambridge University Press.
Short and insightful tour of the subject.

C. Itzykson and J-B. Zuber, Quantum Field Theory, reissued in Dover Books on Physics.
A classic. While somewhat dated, it contains an impressive amount of information. Still extremely useful as a reference for many details that cannot be easily found elsewhere.

F. Strocchi, An Introduction to Non-Perturbative Foundations of Quantum Field Theory, Oxford Science Publications.
More specialized and mathematical. These lecture notes give a clear introduction to various approaches to the axiomatic foundations of QFT. 

Contacts: leonardo.rastelli{at} Office:  Math Tower 6-115B.

Teaching Assistant:  Kostantinos Roumpedakis   konstantinos.roumpedakis{at}

Lectures: Wed and Friday, 12noon-1:20pm in P116

Office Hours: 
Lecturer: By appointment. Send me an email or talk to me after class.

Some Notes and Papers: 



The homework is due in class.  Discussion of the homework is encouraged but each of you must submit a personal solution.

HW1   (due Wed Sept 13)


HW2   (due Wed Sept 27)


HW3 (due Wed Oct 4)


HW4 (due Friday Oct 13)


HW5 (due Wed Oct 25)


HW6 (due Wed Nov 15)


HW7 (due Monday Nov 27)


HW8 (due Friday Dec 8)


Midterm:  November 1, in class





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