PHY 610

Quantum Field Theory I

Lecturer: Leonardo Rastelli

Welcome to the home page of QFT I for Spring 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.

There are simply too many fundamental ideas and techniques for a two-semester course to be comprehensive. My aim in this first semester will be to expose you as fast as possible (but hopefully not faster) to the basic formalism and techniques of perturbative quantum field theory: field quantization (both in the canonical and path-integral approach), Feynman diagrams, symmetries, the basics of renormalization theory. We will apply the formalism mostly to particle physics examples, with the goal of covering some of the classic calculations of Quantum Electrodynamics (the quantum theory of light and electrons) by the end of the semester. (The physics of non-abelian gauge fields and the Standard Model of particle physics will be covered in the second semester.) But we will also see how to apply QFT to the calculation of critical exponents in statistical mechanics. That the same formalism should predict the scattering of relativistic particles and the critical exponents of boiling water is one of the main wonders of the subject.

Course Outline: The necessity of the field viewpoint. Canonical quantization of the scalar field. Symmetries and Noether's theorem. Path-integral quantization. Diagrammatics: connected, 1P1, Feynman rules. S-matrix and cross sections. Representations of the Poincare' group. Canonical and path-integral quantization of spinors. Abelian gauge fields. Quantum Electrodynamics (QED). Tree-level processes in QED. Renormalization of scalar field theory. The renormalization group. The Wilson-Fisher fixed point and critical exponents. If time permits: spontaneous breaking of global symmetries; Coleman-Weinberg potential.

Books:

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.

T. Lancaster and S. J. Blundell, Quantum Field Theory for the Gifted Amateur, Oxford University Press.
Very pedagogic treatment of basic QFT.

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.

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

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}stonybrook.edu. Office: Math Tower 6-115B.

Teaching Assistant: Di Wang, di.wang.2{at}stonybrook.edu Office: Physics D-120

Lectures: Wed and Friday, 11:30am-12:50pm in Math 6-125 (YITP common room)

Office Hours:
TA: Monday and Tuesday 12-1pm in Physics D-120
Lecturer: Wed 1:30-3pm in 6-115B, but please alert me beforehand (very short notice ok, I'll be around in the YITP). Or send me an email to setup another time or talk to me after class.

Some Notes: Lecture1

RubakovChapt3

HallChapt16

SpinorReferences

PolchinskiPaper

WeinbergPaper

StatisticalQFT

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

HW1 (due Feb 3)

HW2 (due Feb 10)

HW3 (due Feb 22)

HW4 (due March 1)

HW5 (due March 8)

HW6 (due March 22)

HW7 (due April 5)

HW8 (due April 12)

HW9 (due April 19)

HW10 (due May 5)

Midterm Exam March 22, in class

MidtermSolutions

Final Exam May 9, in class

Final Exam

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