]> grading Homeworks, a take-home mid-term, and a final exam; the grades will be based on these (60%/20%/20%). Exams and homeworks include optional problems ("bonus" = extra credit). Homework assignments will be posted on the web every Thursday, due Tuesday, and by graded by your fellow students by the next Tuesday. August 21 1. Lattice Field Theory Diffusion as a sum over Paths chapterName Chapter 1 Lattice Field Theory Cvitanović lecture notes ZeeChap1 A. Zee Chapter I.1 Who Needs It? From A. Zee "Quantum Field Theory in a Nutshell" ItzDrouffe C. Itzykson and J.-M. Drouffe Statistical field theory, vol 1 (Cambridge U. Press, 1991) Chapter 1: From Brownian motion to Euclidean fields (A nice discussion of free propagation as Brownian walks) August 23 2. Discrete Fourier transforms Fourier modes as eigenmodes of translation chapterName Chapter 1 Lattice Field Theory Cvitanović lecture notes #1 problems - due Tue Aug 28, in class August 28 3. Green's function in Quantum Mechanics chapterName Chapter 2 Path integral formulation of Quantum Mechanics Cvitanović lecture notes chapterKadanoff L.P. Kadanoff Statistical Physics; Statics, Dynamics and Renormalization Chapter 3: Gaussian Distributions (available online) PhysicsTodRev Physics Today review August 30 4. Path integral - Quantum Mechanics ZeeChap2 A. Zee Chapter 2 Path integral formulation of Quantum Mechanics #2 problems - due Tue Sep 4, in class September 3 Labor Day September 4 5. Dirac-Feynman's Formulation of Quantum Mechanics QM amplitudes as a sum over paths chapterName Chapter 3 Path integral formulation of Quantum Mechanics Cvitanović lecture notes chapterName Chapter 6 Path Integrals in Quantum Mechnics M. Srednicki book September 6 6. Collective excitations Elastodynamic equilibria of 1- and 2-dimensional solids. Phonons. ZeeChap3 A. Zee Chapter I.3 From Mattress to Field chapterName Section 1.6 Collective excitations: from particles to fields Cvitanović lecture notes #0 template If you like to write up your solutions in LaTeX, here is a template #3 problems - due Tue Sep 11, in class September 11 7. Quefithe Quefithe Fable Quefithe QFTchap2 Chapter 2 Generating functionals What the mole saw September 13 8. Quefithe Dyson-Schwinger equations QFTchap2F Chapter 2 Connected, 1PI Green's functions Tying the Nudo del Diablo #4 problems - due Tue Sep 18, in class September 18 9. Quefithe QFTchap3 Chapter 3 Path Integrals What the crow saw September 20 10. Quefithe What the fox saw: it's just a Fourier transform. Tree expansions: Saddle point evaluation of path integrals, one loop (leading h-bar) corrections. Ward identities: symmetries relate and constrain different Green's functions. Quefithe Review by Feynman chapterName Chapter 5 Field theory path integrals Cvitanović lecture notes #5 problems - due Tue Sep 25, in class September 25 11. Perturbation expansions are asymptotic Formally, perturbation series is always asymptotic, but can be very accurate. chapterName Section 5.6 Saddle-point expansions are asymptotic Cvitanović lecture notes FiniteFieldTheo QED is it finite, not asymptotic? September 27 12. Scalar field theory The first physical result: Yukawa interaction by scalar fields (mesons) is attractive. ZeeChap3 A. Zee Chapter I.3 From Mattress to Field ZeeChap4 A. Zee Chapter I.4 From Field to Particle to Force #6 problems - due Thu Oct 11, in class October 2 13. Scalar field theory ZeeChap5 A. Zee Chapter I.5 Coulomb and Newton: Repulsion and Attraction ZeeChap11 A. Zee Chapter I.11 Field Theory Redux October 4 14. Effective action While the full partition function for bare particle interactions is the easiest to derive, the physical content of a theory is given by the `effective action', the interctions between dressed particles (this is a continuation of lecture 9, a deeper dive). QFTchap2F Sections 2.H and 2.I 1PI Green's functions, vacuum bubbles The 1pI generating functional is the Lagendre transform of the connected diagrams generating functional. QFTchap3 Sections 3.E and 3.H Legendre transforms The 1pI generating functional can be interpreted as the `effective' (or `quantum') action functional. #7 problems - due Thu Oct 18, in class October 8-9 fall recess October 11 15. The Dirac Equation ZeeChapII1 A. Zee Chapter II.1 The Dirac Equation GreiReinDirac W. Greiner and J. Reinhardt Dirac equation The excerpt in ChaosBook.org/library (click on Field Theory link) covers Dirac's original derivation of his equation. October 16 16. Midterm All material covered in the 1. part of the course, up to fall recess: generating functions, path integrals, their perturbative expansions, scalar fields propagators. midterm - usual time, in class midterm grades distribution [all solutions are in the book] October 18 17. SU(2) and SO(3) Spin 1/2 is hiding in our Euclidean 3D space in plain sight, and nature has chosen to us it. Its representation theory will carry over also to the Minkowsky spacetime SO(1,3). SU2SO3 Notes 11.1 SU(2) and SO(3) SU(2) - SO(3) correspondence HarterHamilt W.G. Harter Hamilton's turns (for fun only) How Hamilton (who would have guessed...) used quaternions to to extend the discrete Fourier transform from a circle to a sphere. #8 problems - due Thu Oct 25, in class October 23 18. SO(1,3) and SU(2) x SU(2) Penr04-24 Roger Penrose Dirac's electron and antiparticles From "The Road to Reality". Skim through Chapt 24, read at least starting with section 24.7 The Dirac equation. Penr04-25 Roger Penrose The standard model of particle physics From "The Road to Reality". Skim through Chapt 25 at your pleasure, none of this will be on the final exam :) Schwicht15-3 Jakob Schwichtenberg SO(1,3) and SU(2) x SU(2) Refresh your QM, sect. 3.6 SU(2). Then work through the commutators of sect. 3.7 The Lorentz Group SO(1,3). Make sure you know the distinction between Weyl, Majorana and Dirac spinors. Can skip sects. 3.7.11 Infinite-Dimensional Representations and 3.8 The Poincare Group, but do read sect. 3.9 Elementary Particles in preparation for learning about the Standard Model. October 25 lecturer: B.F.L. Ward 19. Celebrating 50 years of the Standard Model The role of Quantum Field Theory loop corrections in establishing the validity of the Standard Model (which David Gross now wants us to call the Standard Theory, in view of its experimental validation). Hossenfelder1 Sabine Hossenfelder String theory So you want to be a string theorist? Here are pros and cons. #9 problems - due Tue Nov 6, in class October 30 20. gamma mu nu gymnastics KapDirac V. K. Dirac Matrices and Lorentz Spinors The signature of the Minkowsky metric makes Lorentz transformations not unitary, and thus (complex conjugate transpose spinor) x (complex spinor) is not a scalar under Lorentz transformations KapDirProp V. K. Propagator for the Dirac Spinor Field is perhaps what you would expect it to be PesSch95chap3 Chapter 3 Dirac equation From Peskin and Schroeder, "An Introduction to Quantum Field Theory"; study pp. 35-44, 49-52, 62-63, rest we'll skip. November 1 21. Feynman rules Zee03appC-D A. Zee Appendices C and D Feynman rules #10 problems - due Thu Nov 8 lecturer: Brian Swingle November 6 22. How to calculate a signature of chaos in field theory using diagrams This material ties into Swignle's 11:15am Theoretical Physics Seminar. Go hear it :) ChoSwi17 Debanjan Chowdhury and Brian Swingle Onset of many-body chaos in the O(N) model The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. November 8 23. Feynman rules Lecture25a P. Cvitanovic Feynman rules part I Apologies for bad audio - thsi was the first test of recording online lectures. Mouse over video's top edge to change the resolution. Lecture25b P. Cvitanovic Feynman rules part II Big day: our first QED Feynman integral. Click on video's gearwheel, lower right edge, to change the resolution. #11 problems - due Thu Nov 13, in class November 13 24. Electron magnetic moment Zee03pp438 A. Zee Chapter VIII.3 The treshold of ignorance ZeeMagMom A. Zee Chapter III.4-6 Electron magnetic moment Skim through Chapt III.4-5, work through Chapt III.6 Sect "Dirac's triumph". Lecture26a P. Cvitanovic Electron magnetic moment (Dirac triumph) (part 1) Big day: our first QED Feynman integral. Click on video's gearwheel, lower right edge, to change the resolution. Lecture26b P. Cvitanovic Electron magnetic moment (Dirac triumph) (part 2) Dirac explains a factor of 2 in observed electron magnetic moment. Lecture26c P. Cvitanovic Electron magnetic moment (Dirac triumph) (part 3) Schwinger's vertex. November 15 25. Feynman Diagrams DKaiser D. Kaiser Physics and Feynman's Diagrams American Scientist 93, 156 (2005) KDThomas Kelly Devine Thomas Feynman Diagrams and the Evolution of Particle Physics The Institute Letter, I.A.S. (Spring 2009) DasGroupCommRels P. Cvitanovic a very brief history of diagrammatics (worth a glance) A lighting fast way to compute commutators, but you have to learn how to draw first. See page 38. LDixon L. Dixon Look ma - no Feynman's diagrams! How we calculate amplitudes these days (October 3, 2013) #12 problems - due Tue Nov 20, in class November 15; recorded July 25, 2013 lecturer: Edward Witten 25 extra Feynman Diagrams in String Theory WittenFeynmDia video What any physicist should know even if she does not want to do mess with strings. NYRevDyson Freeman J. Dyson The World on a String To balance the pied piper song - a delightful sceptic's view. November 20 lecturer: Ignacio Taboada 26. Standard Model DasGroupFeynmDiag Apostolos Vasileiadis Symmetry (for fun only) Gauge invariance is not preserved! no problem - none due this week November 21-23 Thanksgiving November 27 27. Electron magnetic moment ZeeMagMom A. Zee Chapter III.6 Electron magnetic moment Work through Chapt III.6 Sect "Schwinger's triumph". SchwartzMagMom Matthew Schwartz Chapter III-3: The anomalous magnetic moment Complementary, even more compact than Zee's derivation. Zee03appC-D Appendices C and D Feynman rules Referred to in calculations of Chapt III.6. Lecture27 P. Cvitanovic Anomalous electron magnetic moment (Schwinger's triumph) Schwinger's \alpha/2\pi calculation sketched out. (You'll have to screw up the volume, sorry.) Styer12 Dan Styer Calculation of the anomalous magnetic moment of the electron The accuracy available as of 21 June 2012 "is the equivalent of measuring the distance from Los Angeles to New York to within the width of a bacterium, or of measuring the distance from the Earth to the Moon to within the width of a single human hair." Kinoshita10 Toichiro Kinoshita Fine Structure Constant, Electron Anomalous Magnetic Moment, and Quantum Electrodynamics The heroic calculation of Toichiro Kinoshita: status as of 2010. [Schwinger's headstone] November 29 28. Gauge invariance Ward identities: symmetries relate and constrain different Green's functions. QFTchap3 Sections 3.G and 3.H Point transformations ZeeMagMom A. Zee Chapter III.4 Gauge invariance: A photon can find no rest QFTchap6 Sections 3.A and 3.B Ghoulies and ghosties ShWi06 A. Shapere and F. Wilczek Geometry of self-propulsion at low Reynolds number (Not covered in this lecture, but might interest you:) From swimming to gauge potentials. But what is a photon, really? ShWi06 The base space (space of unlocated shapes) for cats A fibration and a base space :) #13 problems - due Tue Dec 4, in class December 4 29. Renormalization CvitQFTparametric Chapter * Parametric representation Unpublished notes: momentum space Feynman integrals, parametric representation. CvitQFTrenorm Chapter * Renormalization Unpublished notes: Power counting, UV divergences, subtractions, counterterms. CvitQFTdisease Chapter * Gauge-invariant sets Unpublished notes: high-orders diseases; gauge set counting; finitness conjecture. December 4 GT classes end Final exam syllabus An overview of material covered by the final exam. [current grades - alert me if I am missing some homework grades] December 6 - freebie 30. Gribov copies NickCave Higgs Boson blues NickCave Nick Cave and The Bad Seeds The full length version December 10 final exam 2:40pm - 5:30pm closed book, closed lecture notes. [course grades] until December ? course opinion survey CIOS web link October 29 - December 14 spring registration PHYS-7143 PHYS-7143 Group Theory The Spring 2019 group theory course can be described this way: Suppose someone came to you and asked, "On planet Z, mesons consist of quarks and antiquarks, but baryons contain three quarks in a symmetric color combination. What is the symmetry group?" The answer requires some thought, and leads to magic that beguiles field theorists. We might get to the answer by the end of the course - but our focus will be on basic tools of group theory: finite groups, subgroups, cosets, and conjugacy, group of permutations, matrix representations, tensors, Schur's Lemma, characters and character table construction, irreducible representations, Lie groups, rotations and why you need no Clebsch-Gordon coefficients. Hope you will join me. Tell your friends to join us too. December 17 GT grades due at noon December 24 the future looks bright Future's So Bright, I Gotta Wear Shades [click right, open in new tab]