PHY 610

                                         Quantum Field Theory I

                                                           Lecturer: Leonardo Rastelli 



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.

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.

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.

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

Teaching Assistant: JP Ang  jianpeng.ang{at} Office: A107

Lectures: Tuesday and Thursday, 11:30am-12:50pm in Room P-129

Office Hours. Lecturer:  in Math Tower 6-115B, Tuesday 2:30pm-4pm or by appointment.
                        TA:  Thursday 1-2pm  in A107 or by appointment

Lectures Outlines:  Lecture 1
                                 Lectures 2, 3  

Lecture 4 
                                 Lecture 5
                                 Lecture 6
                                 Lecture 7                            


The homework problem sets will be usually assigned each Tuesday and due the following Tuesday in class. 

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


                      HW1 (due Feb 10 in class):   HW1


                      HW2 (due Feb 17 in class):  HW2

                      HW3 (due Feb 24 in class): HW3


                       HW4 (due March 3 in class): HW4


                      HW5 (due March 10 in class):HW5



                      HW6 (due April 7 in class):HW6

                      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


Final Exam May 13,  5:30-8pm, in the usual classroom. You are allowed to bring a formula sheet of A4 size, filled on a single side.

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.

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