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Course11510444675 lectures

Tapestry of Field theory: Classical & Quantum, Equilibrium & Nonequilibrium Perspectives

Prof. Mahendra K. Verma · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1 : Introduction to Field Theory and Course Video
  2. Lecture 2 : Complex Variables+ Integration Video
  3. Lecture 3 : Cauchy Principal value theorem Video
  4. Lecture 4 : Fourier Transform Video
  5. Lecture 5 : Green's function and examples Video
  6. Lecture 6 : Green's function in fourier space: Poisson equation Video

Week 2

  1. Lecture 7 : Fourier transform, time frequency Video
  2. Lecture 8 : Green's function (Helmholtz and wave equation ) Video
  3. Lecture 9 : Green's function (Diffusion and Schrodinger equation) Video
  4. Lecture 10 : Dimensional Analysis Video
  5. Lecture 11a : Functionals (Lagrangian for particles) Video
  6. Lecture 11b : Lagrangian formalism Video
  7. Lecture 12 : Relativistic fields Video
  8. Lecture 13 : Hamiltonian formalism Video
  9. Lecture 14 : Lagrangian formalism (Least action principle) Video
  10. Lecture 15 : Relativistic fields revisited Video

Week 3

  1. Lecture 16 : Noether's theorem and Symmetries Video
  2. Lecture 17 :Review of Quantum mechanics Video
  3. Lecture 18 : Second Quantization Video
  4. Lecture 19 :Field Operators Video
  5. Lecture 20 : Fock Space and vaccum Energy Video
  6. Lecture 21 : Quantization of Bosons and Fermions Video
  7. Lecture 22 : Examples Video

Week 4

  1. Lecture 23 : Free Fermi gas Video
  2. Lecture 24 : Propagators and perturbations Video
  3. Lecture 24 : Relativistic quantum field theory Video
  4. Lecture 26 : Feynman Propagator Video

Week 5

  1. Lecture 27 : Review of Statistical Mechanics (Partition Function) Video
  2. Lecture 28 : Feynman Path Integral Video
  3. Lecture 29 : Diagrammatic Field Theory (Wick's Theorem) Video
  4. Lecture 30 : Wick's Theorem (Continuation) Video
  5. Lecture 31 : Diagrammatic Perturbation Theory Video
  6. Lecture 32 : Green's Function and Correlation Function Video
  7. Lecture 33 : Feynman Diagrams Video

Week 6

  1. Lecture 34 : Phase Transition and Landau Theory Video
  2. Lecture 35 :Failure of Landau's Theory Video
  3. Lecture 36 : Scale Invariance Video
  4. Lecture 37 : Renormalization group - preliminary Video
  5. Lecture 38 : RG Steps Video

Week 7

  1. Lecture 39 : Perturbative Calculations Video
  2. Lecture 40 : RG fixed points Video
  3. Lecture 41 : Relevant and Irrelevant variables Video
  4. Lecture 42 : Behavior Near critical points Video
  5. Lecture 43 : Computing Critical Exponents Video

Week 8

  1. Lecture 44 : Running coupling const: phi^4 theory Video
  2. Lecture 45 : Charge and mass renormalization: QED & QCD Video
  3. Lecture 46 : Breaking a Continuous Symmetry (Goldstone Mode) Video
  4. Lecture 47 : Covariant Electrodynamics (Gauge Interactions) Video
  5. Lecture 48 : Higgs Mechanism Video

Week 9

  1. Lecture 49 : Introduction to Non-Equilibrium Field Theory (Langevin Equation) Video
  2. Lecture 50 : Fluctuation Dissipation Theorem Video
  3. Lecture 51 : Kolmogorov's Theory of Turbulence Video
  4. Lecture 52 : Equilibrium and Non equilibrium Solution of Navier Stokes Video
  5. Lecture 53 : Energy Flux in Navier Stokes Equation Video

Week 10

  1. Lecture 54 : RG shell model Video
  2. Lecture 55 : RG shell model contd Video
  3. Lecture 56 : Renormalization of the coupling constant for the shell model Video
  4. Lecture 57 : Flux Computation for the Shell Model of Turbulence Video
  5. Lecture 58 : Renormalization Group Analysis of Navier Stokes Equation Video
  6. Lecture 59 : Flux Computation for the Navier Stokes Equation Video

Week 11

  1. Lecture 60 : Functional Form of a Dynamical Equation Video
  2. Lecture 61 : Surface Growth Phenomena : Introduction Video
  3. Lecture 62 :Surface Growth Phenomena : EW equation Video
  4. Lecture 63 : Surface Growth Phenomena : KPZ equation Video
  5. Lecture 64 : Surface Growth Phenomena : KPZ continued Video
  6. Lecture 65 : RG prodecure for KPZ equation Video
  7. Lecture 66 : Noise Renormalization Video
  8. Lecture 67 : Fixed Point Solution Video

Week 12

  1. Lecture 68 : Weak Turbulence Theory using examples Video
  2. Lecture 69 : Weak Turbulence Applications (Rotating Turbulence, Internal and Surface Gravity Waves) Video
  3. Lecture 70 : Nonlinear Schrodinger Equation Video
  4. Lecture 71 : Field Theory of Passive Scalar Turbulence Video
  5. Lecture 72 : Course Summary Video

Live Session

  1. Live Session 24-02-2024 Video
  2. Live Session 22-04-2024 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Physics
Teacher
Prof. Mahendra K. Verma
Level
Undergraduate
Language
English
Subjects
Physics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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