** **

**
**

Welcome to the home page of QFT I for Spring 2015. 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:** (Optimistic!) 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. Spinor-helicity formalism.
Renormalization of scalar field theory. The renormalization group. The
Wilson-Fisher fixed point and critical exponents. Spontaneous breaking of
global symmetries. Coleman-Weinberg potential.

The main references will be the recent books by Srednicki and Schwartz:

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.

M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press.

Good modern textbook, building up to a comprehensive treatment of the Standard Model.

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. 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.

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.

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.

TA: Thursday 1-2pm in A107 or by appointment

Lectures 2, 3

Lecture 5

Lecture 6

PathIntegralNotes

Lectures8,9

Lectures13-19

Homework:

Discussion of the homework is encouraged but each of you must submit a personal solution.

HW1 (due Feb 10 in class): HW1

HW3 (due Feb 24 in class): HW3

HW4 (due March 3 in class): HW4

HW5 (due March 10 in class):HW5

HW7 (due April 14 in class): HW7

HW8 (due April 21 in class): HW8

HW9 (due April 28 in class): HW9

HW10 (due May 7 in class): HW10

**Midterm Exam**
March 24, in class

**Americans with
Disabilities Act:**

If you have a physical, psychological, medical
or learning disability that may impact your course work, please contact
Disability Support Services, ECC (Educational Communications Center)
Building, room128, (631) 632-6748. They will determine with you what
accommodations, if any, are necessary and appropriate. All information and
documentation is confidential.

**Academic
Integrity:**

Each student must pursue his or her academic
goals honestly and be personally accountable for all submitted work.
Representing another person's work as your own is always wrong. Faculty
are required to report any suspected instances of academic dishonesty to
the Academic Judiciary. Faculty in the Health Sciences Center (School of
Health Technology & Management, Nursing, Social Welfare, Dental
Medicine) and School of Medicine are required to follow their
school-specific procedures. For more comprehensive information on
academic integrity, including categories of academic dishonesty, please
refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

**Critical Incident
Management:**

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.