]> grading The course grade is based on homeworks. Homeworks include optional problems ("bonus" = extra credit). Homework assignments will be posted on the web every Wednesday, due next Wednesday, uploaded as pdf files on Canvas, and graded by your fellow students by the following Monday. Solution sets will be posted on canvas every Wednesday. January 8 1. Lattice Field Theory Diffusion as a sum over Paths chapterName1 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 (optional) C. Itzykson and J.-M. Drouffe Statistical field theory, vol 1 Chapter 1: From Brownian motion to Euclidean fields (A nice discussion of free propagation as Brownian walks) January 10 2. Discrete Fourier transforms Fourier modes as eigenmodes of translation chapterName Chapter 1 Lattice Field Theory Cvitanović lecture notes #0 template If you like to write up your solutions in LaTeX, here is a template #1 problems - due Wed Jan 17, on Canvas January 15 MLK Day January 17 3. Discrete Fourier transforms Fourier modes as eigenmodes of translation chapterName Chapter 1 Lattice Field Theory Cvitanović lecture notes #2 problems - due Wed Jan 22, on Canvas January 22 4. Discrete Fourier transforms Fourier modes as eigenmodes of translation chapterName Chapter 1 Lattice Field Theory Cvitanović lecture notes chapterBernard20p16 (optional) D. Bernard Statistical Field Theory and Applications P. 16 : Scaling limit of free random paths January 24 5. Green's function in Quantum Mechanics chapterName Chapter 2 Path integral formulation of Quantum Mechanics Cvitanović lecture notes ZeeChap2 (optional) A. Zee Chapter 2 Path integral formulation of Quantum Mechanics chapterKadanoff (optional) L.P. Kadanoff Statistical Physics; Statics, Dynamics and Renormalization Chapter 3: Gaussian Distributions (available online) PhysicsTodRev (optional) Physics Today review #3 problems - due Wed Jan 31, on Canvas January 29 6. 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 (optional) Chapter 6 Path Integrals in Quantum Mechnics M. Srednicki book January 31 7. Quefithe Quefithe Fable Quefithe What the mole saw QFTchap2 Chapter 2 Generating functionals Brookhaven (optional) Flying to Brookhaven with box-fulls of cards I have a crank theory that perturbation series for g-2 is not an asymptotic series. #4 problems - due Wed Feb 7, on Canvas February 5 8. Dyson-Schwinger equations GenFunct Chapter 2 Generating functionals Sects. A-D Going fishing: inidices, vertices, Feynman diagrams February 7 9. Generating functionals QFTchap2b Chapter 2 Generating functionals Sects. E-J Tying the Nudo del Diablo: Full, connected, 1PI Green functions #5 problems - due Wed Feb 21, on Canvas February 12 10. Partition function QFTchap3 Chapter 3 sects. A, B Path Integrals What the crow saw: It's a Fourier transform. It always has been. Costello18sect2 (optional) Costello sect. 1.2 Functional integrals in quantum field theory Costello's summary of this part of the course. February 14 11. Wick expansion What the fox saw: it's the most tedious way to generate Feynman diagrams and their combinatori weights. Quefithe Review by Feynman QFTchap3a Chapter 3 sects. C-H Path Integrals Wick, tree, saddlepoint expansions #6 problems - due Wed Feb 21, on Canvas February 19 12. 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 (optional) 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 (optional) Francois David Quantum Field Theory 2 2023/24 Our course follows the French school. Here is the real deal. Costello1-2 (optional) Costello lectures 1, 2 Laplacians, propagators Are discrete derivatives causing you discomfort? Try Costello. February 21 13. 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'. 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 Wed Mar 6, on Canvas February 26 14. Perturbation expansions are asymptotic Formally, perturbation series is always asymptotic, but can be very accurate. chapterName Section 5.6 Saddle-point expansions are asymptotic Tree expansions: Saddle point evaluation of path integrals, one loop (leading h-bar) corrections. Ward identities: symmetries relate and constrain different Green's functions. FiniteFieldTheo QED is it finite, not asymptotic? February 28 15. Deterministic lattice field theory Deterministic solutions form the backbone of the WKB semi-classical approximation to the quantum path integral. LC21 Liang and Cvitanović (2022) sect 2. A fair coin toss: Bernoulli map, temporal Bernoulli An excerpt from Liang and Cvitanović paper: instead of "1.1 Wanderings of a drunken snail" of lecture 1, now the law is deterministic, leading to walks that are chaotic. #8 problems - due Wed Mar 6, on Canvas March 4 16. Deterministic lattice field theory Deterministic solutions form the backbone of the WKB semi-classical approximation to the quantum path integral. Chapter6 Chapter 6 sect 6.2, sect 6.3 Temporal Bernoulli, determining periodic states. March 6 17. Three ways to climb that Hill Deterministic solutions form the backbone of the WKB semi-classical approximation to the quantum path integral. Chapter6a Chapter 6 sects 6.4, 6.5, 6.7 Orbit stability, Hill determinants, reciprocal lattice. #9 problems - skipped March 11 18. Collective excitations Elastodynamic equilibria of 1- and 2-dimensional solids. Phonons. ZeeChap3 A. Zee Chapter I.3 From Mattress to Field chapterName (optional) Section 1.6 Collective excitations: from particles to fields Cvitanović lecture notes March 13 19. Scalar field theory over continuum The first physical result: Yukawa interaction by scalar fields (mesons) is attractive. ZeeChap4 A. Zee Chapter I.4 From Field to Particle to Force ZeeChap5 (optional) A. Zee Chapter I.5 Coulomb and Newton: Repulsion and Attraction Fun, but it requires more knowledge about particles with spins than what we have at this stage. Might revisit. #10 problems - skipped March 18-22 Spring break March 25 20. The Dirac equation ZeeChap11 A. Zee Chapter I.11 Field Theory Redux All material covered in the 1. part of the course, up to fall recess: generating functions, path integrals, their perturbative expansions, scalar fields propagators. ZeeChapII1 A. Zee Chapter II.1 The Dirac equation chapterName (optional) M. Srednicki Chap. 1, p. 4 Attempts at relativistic quantum mechanics An overview of the origin of Dirac's approach to combining quantum mechanics and relativity. GreiReinDirac (optional) W. Greiner and J. Reinhardt Dirac equation The excerpt in covers Dirac's original derivation of his equation. March 27 21. Gamma matrices CrossFit I agree with Hamilton. His deepest insight was not his teenage work on Hamiltonian dynamics, but his adult year's discovery of quaternions. SU2SO3 Notes 11.1 SU(2) and SO(3) SU(2) - SO(3) correspondence. 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). KapDirac (optional) Vadim Kaplunovsky 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 birdtracksEUcourse3 (optional) P. Cvitanović "Group Theory" Lect. 11 - SU(2) and SO(3); Lect. 12 - Lorentz group; spin We do not have time to cover this material in classroom. I cover it in videos linked to my group theory lecture notes. #11 problems Exer. 11.2 - due Wed Apr 10, on Canvas Timeless Extra. SO(1,3) and SU(2) x SU(2) Our course is too compressed to cover all this great stuff - but if you find some time, you might enjoy reading Penrose and Schwichtenberg. Penr04-24 (optional) 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 (optional) Roger Penrose The standard model of particle physics From "The Road to Reality". Skim through Chapt 25 at your pleasure, none of this would be on the final exam :) Schwicht15-3 (optional) 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. April 1 22. QED Feynman rules Includes mumbling about constraints implemented as negative dimensions; fermions, ghosts, supersymmetries QFTchap4 (optional) Chapter 4 Fermions read sects. A, B, C email7 what you need to know about fermions :) QFTchap6 (optional) Sections 3.A and 3.B Ghoulies and ghosties April 3 23. QED Feynman rules QED Feynman rules: momentum photon, electron propagators. KapDirProp Vadim Kaplunovsky Propagator for the Dirac Spinor Field is perhaps what you would expect it to be Zee03appC-D A. Zee Appendices C and D Feynman rules #12 problems - due Wed Apr 17 on Canvas April 8 24. Feynman integrals CvitQFTparametric P. Cvitanović: Parametric representation Chaosbook.org/FieldTheory/pdf.html : momentum space Feynman integrals, parametric representation. CviKin74a (optional) P. Cvitanović and T. Kinoshita, Feynman-Dyson rules in parametric space A pedagogical overview of the Schwinger-Feynman parametric representation of Feynman integrals, should be useful for any QFT perturbative calculation. April 10 25. The anomalous magnetic moment QFTblog (optional) P. Cvitanović QFT and its discontents : a blog Is QED finite? The numerical evidence is suggestive, but no theory so far. #13 problems - due Wed Apr 17 April 15 26. Electron vertex diagram Zee03pp438 (optional) A. Zee Chapter VIII.3 The treshold of ignorance SchwartzMagMom Matthew Schwartz Chapter III-3: The anomalous magnetic moment Complete the evaluation of the denominator, eqq. (16). April 17 27. Schwinger's triumph: Anomalous electron magnetic moment SchwartzMagMom Matthew Schwartz Chapter III-3: The anomalous magnetic moment Evaluate the numerator, eq. (16). Integrate the loop momentum, eq. (24). Derive the Schwinger correction, eq. (26). 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". #14 problems - due Mon Apr 22, on Canvas [Schwinger's headstone] April 22 28. Deterministic turbulence as the WKB backbone for strongly nonlinear field theories WKB approximation to a QFT partition function is given by all solutions of theory's deterministic Euler-Lagrange equations. Can any be determined for theories such as QCD, or gravity? 240422lecture P. Cvitanović: Slides for the lecture. tutorials (Optional) Movies of plane Couette flow. Geometry of turbulence in wall-bounded shear flows: a stroll through 61,506 dimensions 240422lecture (Optional) P. Cvitanović: Chaotic Field Theory: a sketch. Program whose goal is a theory of turbulent dynamics of classical, stochastic and quantum fields, developed in two directions: 1) explorations of the feasibility of describing weak turbulence in terms of spatiotemporally recurrent patterns, and 2) new perturbation theory methods for computing corrections about nontrivial saddles of path integrals. April 25 no final exam a freebie 29. Gribov copies blues May 6 GT grades due at noon May 6 have good holidays! until May 6 course opinion survey CIOS web link May 8 the future looks bright Future's So Bright, I Gotta Wear Shades [click right, open in new tab] ' the rest has yet to be worked out Timeless 28. Feynman Diagrams DKaiser (optional) D. Kaiser Physics and Feynman's Diagrams American Scientist 93, 156 (2005) KDThomas (optional) Kelly Devine Thomas Feynman Diagrams and the Evolution of Particle Physics The Institute Letter, I.A.S. (Spring 2009) DasGroupCommRels (optional) P. Cvitanović 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. (optional) LDixon L. Dixon Look ma - no Feynman's diagrams! How we calculate amplitudes these days (March 3, 2013) Timeless XX extra String Theory (optional) NYRevDyson Freeman J. Dyson The World on a String To balance the pied piper song - a delightful sceptic's view. Timeless XX. Electron magnetic moment ZeeMagMom A. Zee Chapter III.6 Electron magnetic moment Work through Chapt III.6 Sect "Schwinger's triumph". Zee03appC-D Appendices C and D Feynman rules Referred to in calculations of Chapt III.6. 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 (optional) Toichiro Kinoshita Fine Structure Constant, Electron Anomalous Magnetic Moment, and Quantum Electrodynamics The heroic calculation of Toichiro Kinoshita: status as of 2010. freebie XX. 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 ShWi06 (optional) 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? freebie XX. Renormalization 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.