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schwartz@g.harvard.eduContact BioResearchTeachingPeople HOME / Teaching I teach graduate and undergraduate students. When I teach, I like to write detailed lecture notes for my courses. I have done so for Quantum Field Theory (Physics 253a,b/254), Waves (Physics 15c), and Statistical Mechanics (Physics 181). The quantum field theory notes have been incorporated into a textbook Quantum Field Theory and the Standard Model,

The introductory quantum field theory course at Harvard has a long history. It was famously taught by Sidney Coleman for around 3 decades. Some of Coleman's lectures can be found here. My approach to field theory is somewhat different from Coleman's, and most other field theory classes, in that I try to keep a tight focus on connection to experiment. My course focuses on modern methods, such as effective field theories and the renormalization group.

QFT in Zero Dimensions: PDF File Review of the path integral. Free theory and Wick's theorem. Perturbation theory, asymptotic expansions and Feynman diagrams. Supersymmetry and localization. Effective theory of a coupled system.QFT in One Dimension: PDF File The path integral approach to Quantum Mechanics and its relation to the operator approach. Brownian motion and the path integral measure. Effective Quantum Mechanics. 1d Quantum Gravity as the worldline approach to QFT.The Renormalization Group: PDF File Wilson's approach to renormalization. Renormalization group flow. Beta functions, anomalous dimensions and Callan-Symanzik equations. Renormalization group trajectories. Counterterms and the continuum limit. Polchinski's equation. The local potential approximation. Gaussian and Wilson-Fisher fixed points in scalar theory. Zamolodchikov's c-theorem. Perturbative Renormalization: PDF File One loop renormalization of quartic scalar theory. Mass renormalization. The on-shell renormalization scheme. Renormalization of the quartic coupling. Irrelevant interactions and the quantum effective action. Dimensional regularization and the MS-bar scheme. The beta function and triviality. One loop renormalization of QED. Vacuum polarization. Counterterms and the beta function of QED. The Euler-Heisenberg effective action.Symmetries in QFT: PDF File Symmetries and conserved charges in classical field theory. Symmetries of the quantum effective action. Ward-Takahashi identities. Current conservation in QFT. Emergent symmetries. Low energy effective field theory. Charges, quantum states and representations. Classical Yang-Mills Theory: PDF File Principal bundles and vector bundles. Connections, curvature and holonomy. The Yang-Mills action and Yang-Mills equations. Matter and minimal coupling. The Yang-Mills path integral. Gauge transformations are redundancies, not symmetries.Perturbative Non-Abelian Gauge Theory: PDF File Faddeev-Popov ghosts and gauge fixing. BRST transformations and their Ward-Takahashi identities. BRST cohomology and the physical Hilbert space. Feynman rules in Lorenz gauge. Vacuum polarization diagrams in Yang-Mills theory. Background field method. The beta function and asymptotic freedom. Topological terms and the vacuum angle.Problem SheetsProblem Sheet 1: PDF File Problem Sheet 2: PDF File Problem Sheet 3: PDF File Problem Sheet 4: PDF File If you're enrolled on the Part III/ MASt course in either Maths, Physics or Astrophysics you can sign up for problem classes here.

This course is the first quarter of a 2-quarter graduate-level introduction to relativistic quantum field theory (QFT). The focus is on introducing QFT and on learning the theoretical background and computational tools to carry out elementary QFT calculations, with a few examples from tree-level quantum electrodynamics processes. The course will be broadly based on the first 13 chapters of Matthew Schwartz's ``Quantum Field Theory and the Standard Model''.

Itzykson C., Zuber J.B., Quantum field theory. One of my personal favourites. The book is very precise (on the level of rigour of physics), and it contains dozens of detailed and complicated derivations that most books tend to omit. I'm not sure this book is very good as an introduction; the first few chapters are accessible but the book quickly gains momentum. Beginners may find the book slightly too demanding on a first read due to the level of detail and generality it contains. Unfortunately, it is starting to have an old feel. Not outdated, but at some points the approach is slightly obsolete by today's standards.

Weinberg S., Quantum theory of fields. As with Coleman, and even more so, the mere name of the author should be a good enough reason to read this series of books. Weinberg, one of the founding fathers of quantum field theory, presents in these books his very own way to understand the framework. His approach is very idiosyncratic but, IMHO, much more logical than the rest of books. Weinberg's approach is very general and rigorous (on the level of physicists), and it left me with a very satisfactory opinion on quantum field theory: despite the obvious problems with this framework, Weinberg's presentation highlights the intrinsic beauty of the theory and the inevitability of most of its ingredients. Make sure to read it at least once.

DeWitt B.S., The global approach to quantum field theory. The perfect book is yet to be written, but if something comes close it's DeWitt's book. It is the best book I've read so far. If you want precision and generality, you can't do better than this. The book is daunting and mathematically demanding (and the notation is... ehem... terrible?), but it is certainly worth the effort. I've mentioned this book many times already, and I'll continue to do so. In a perfect world, this would be the standard QFT textbook.

Zeidler E., Quantum field theory, Vol. 1, 2 and 3. Initially intended to be a six-volume set, although I believe the author only got to publish the first three pieces, each of which is more than a thousand pages long! Needless to say, with that many pages the book is (painfully) slow. It will gradually walk you through each and every aspect of QFT, but it takes the author twenty pages to explain what others would explain in two paragraphs. This is a double-edged sword: if your intention is to read the whole series, you will probably find it annoyingly verbose; if, on the other hand, your intention is to review a particular topic that you wish to learn for good, you will probably find the extreme level of detail helpful. To each their own I guess, but I cannot say I love this book; I prefer more concise treatments.

Bogolubov, Anatoly A. Logunov, A.I. Oksak, I. Todorov, General principles of quantum field theory. A standard reference for mathematically precise treatments. It omits many topics that are important to physicists, but the ones they analyse, they do so in a perfectly rigorous and thorough manner. I believe mathematicians will like this book much more than physicists. For one thing, it will not teach you how (most) physicists think about QFT. A lovely book nevertheless; make sure to check out the index so that you will remember what is there in case you need it some time in the future.

The most complete and comprehensive approach to quantum field theory is certainly Steven Weinberg's series (Volume 1, Volume 2, Volume 3). No prior knowledge is assumed. Everything is explained from first principles. Weinberg has an amazing physical understanding and developed a major part of QFT. If you want to deepen your understanding or if you want to learn everything including important proofs these are the perfect books for you.

It covers relativistic QM thoroughly before developing field theory through canonical quantization.This book is very detailed in its derivation of equations. The author skips very few steps.As a result, this book almost reads like a novel (i.e. easy to read).

Description:These quantum field theory notes include the following topics: Quantization of Field Theory; Theory of Renormalization; Symmetry; Standard Model of Electroweak Interaction; Theory of Strong Interaction -- Quantum Chromodynamics.

The first two are comprehensive textbooks which cover all thecourse material in great detail and much more. Our notation and conventions (but not the order of presentation of the material) tend to follow Peskin and Schroeder's. Zee's book gives apedagogical but not too technical overview of many topics withoutgoing into great depth. Ramond's book is focused on the pathintegral approach to quantum field theory.

Schwarz is one of the pioneers of Morse theory and brought up the first example of a topological quantum field theory.[6] The Schwarz genus, one of the fundamental notions of topological complexity, is named after him. Schwarz worked on some examples in noncommutative geometry. He is the "S" in the AKSZ model (named after Mikhail Alexandrov, Maxim Kontsevich, Schwarz, and Oleg Zaboronski).

A consistent theory of free tachyons has shown how tachyon neutrinos canexplain major cosmological phenomena, Dark Energy and Dark Matter. Now weinvestigate how tachyon neutrinos might interact with other particles: the weakinteractions. Using the quantized field operators for electrons and tachyonneutrinos, the simplest interaction shows how the chirality selection rule, putin by force in the Standard Model, comes out naturally. Then I wander into are-study of what we do with negative frequencies of plane wave solutions ofrelativistic wave equations. The findings are simple and surprising, leading toa novel understanding of how to construct quantum field theories. 2b1af7f3a8