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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.

These lecture notes are based on an introductory course on quantum field theory, aimed at Part III (i.e. masters level) students. The full set of lecture notes can be downloaded here, together with videos of the course when it was repeated at the Perimeter Institute. Individual sections can be downloaded below.

1. Classical Field Theory: Postscript  PDF Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance;Noether's Theorem and Conserved Currents; Hamiltonian Field Theory.2. Canonical Quantization: Postscript  PDF The Klein-Gordon Equation, The SimpleHarmonic Oscillator; Free Quantum Fields; Vacuum Energy; Particles;Relativistic Normalization; Complex Scalar Fields; The Heisenberg Picture;Causality and Propagators; Applications; Non-Relativistic Field Theory 3. Interacting Fields: Postscript  PDF Types of Interaction; The InteractionPicture; Dyson's Formula; Scattering; Wick's Theorem; Feynman Diagrams; FeynmanRules; Amplitudes; Decays and Cross Sections; Green's Functions; Connected Diagramsand Vacuum Bubbles;Reduction Formula 4. The Dirac Equation: Postscript  PDF The Lorentz Group; Clifford Algebras;The Spinor Representation; The Dirac Lagrangian; Chiral Spinors; The WeylEquation; Parity; Majorana Spinors; Symmetries and Currents; Plane Wave Solutions.5. Quantizing the Dirac Field: Postscript  PDF A Glimpse at the Spin-Statistics Theorem; Fermionic Quantization; Fermi-DiracStatistics; Propagators; Particles and Anti-Particles; Dirac's HoleInterpretation; Feynman Rules 6. Quantum Electrodynamics: Postscript  PDF Gauge Invariance; Quantization; Inclusion of Matter -- QED; Lorentz InvariantPropagators; Feynman Rules; QED Processes. Problem SheetsProblem Sheet 1: Postscript  PDF Classical Field Theory Problem Sheet 2: Postscript  PDF Quantizing the Scalar Field Problem Sheet 3: Postscript  PDF The Dirac Equation Problem Sheet 4: Postscript  PDF Scattering AmplitudesQuantum Field Theory on the WebQuantum Field Theory by Michael Luke.Fields by Warren Siegel.Quantum Condensed MatterField Theory by Ben SimonsErrata for the book by Peskin and Schroeder Philip Tanedo, who took this course long ago, has put together auseful literature review of quantum field theory textbooks.

The late Sidney Coleman taught the quantum field theory course at Harvardfor many years, influencing a generation of physicists in the waythey view and teach QFT. Below you can find the pdf files of handwrittenlecture notes for Coleman's course (transcribed by Brian Hill). The notes come in two largefiles, each around 6.5 Mb.

ANNOUNCEMENTSPOSTINGS Homework assignmentsGENERAL INFORMATIONInstructor: Prof. Duiliu-Emanuel Diaconescu Office: Serin E358 Email: duiliu@physics.rutgers.edu Phone: (848) 445-9054 Office hours: By appointment online. Lectures: Tuesday and Thursday, 10:20-11:40am, online via Webex. Textbooks: M.E. Peskin, D.V. Schroeder: An Introduction to Quantum Field Theory M. Srednicki: Quantum Field Theory PDF notes version (similar to the published version) can be found at ~mark/ms-qft-DRAFT.pdf Prerequisites:Physics 618, Fields I. If you did nottake Fields I, it is your responsibilityto do background reading to make sure you understandthe concepts in this course.Specifically, familiarity with the following concepts will be assumed: Canonical quantization of scalar fields (M. Peskin, D. Schroeder: Chs. 2,3) Renormalized perturbation theory (phi^3 and phi^4 theories) (PS: Chs. 4.1-4.4, 4.7, 10.1-10.2) Path-integral quantization of scalar fields (both Minkowski and Euclidean forms)(PS: Chs. 9.1-9.3, 9.5) Renormalization Group (PS: Chs. 12.1-12.3) General form of the spectrum in QFT, S-matrix, LSZ formalism (PS: Chs. 4.5, 4.6, 7.1-7.3) Spontaneous Symmetry Breaking (PS: Ch. 11.1)Homeworks:Homeworks will be assigned at intervals of 1.5 or 2 weeks; theywill be graded and returned to you.Exams:There will be no exams.Students with disabilities:Please read here.DETAILED SYLLABUS This is a tentative schedule of what we will cover in the course. It is subject to change, often without notice. These will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered. Usethis plan to read ahead from the text books,so you are better equipped to ask questions in class. QUANTIZATION OF SPIN 1/2 FIELD Classification of fields with spin: representations of the Lorentz group (Srednicki 34-35) Lagrangians for spin 1/2 fields: Weyl, Majorana, Dirac. Free particle wavefunctions. (Srednicki 36) Canonical quantization, LSZ reduction (Srednicki 37-39, 41) Discrete symmetries (Srednicki 40) Free propagator, fermionic path integrals, Feynman rules, Yukawa theory (Srednicki 42-45) QUANTIZATION OF EM FIELD Canonical quantization: General aspects of quantization of systems with constraints.Maxwell's equations. EM field as a dynamical system with constraints.Quantization in the Coulomb gauge. (Srednicki 33, 54-56) Covariant path integral quantization: Euclidean path integral. Gauge group. Gauge fixing conditions. Faddeev-Popov trick.Feynman propagator. (Peskin 9.4) QUANTUM ELECTRODYNAMICS Lagrangian and Feynman rules: Feynman rules for QED. Gauge invariance of the scattering amplitudes.Electron vertex function (formal structure).(Srednicki 58-59; Peskin 4.7, 5.1, 6.2) One-loop radiative corrections: Electron propagator.Electron vertex function.Ward-Takahashi identity.Magnetic moment of the electron.Infrared divergence.(Srednicki 62-64, 67; Peskin 6.3-6.5, 7.1, 10.3) Renormalized Perturbation Theory: Vacuum polarization: formal structure.Renormalized action and counterterms. Pauli-Villars anddimensional regularizations.Vacuum polarization: evaluation.(Peskin 10.1, 10.3; Srednicki 62) Renormalization group in QED: Radiative corrections to the Coulomb law.Callan-Symanzik equation. Beta-function.(Peskin 10.3, 12.3; Srednicki 66) NON-ABELIAN GAUGE THEORIES

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. 2b1af7f3a8