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Tapestry of Field theory Classical and Quantum Equilibrium and Nonequilibrium Perspectives
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | IIT Kanpur |
The Syllabus
- Introduction to Field Theory and Course
- Complex Variables+ Integration
- Cauchy Principal value theorem
- Fourier Transform
- Green's function and examples
- Green's function in fourier space: Poisson equation
- Fourier transform, time frequency
- Green's function (Helmholtz and wave equation )
- Green's function (Diffusion and Schrodinger equation)
- Dimensional Analysis
- Functionals (Lagrangian for particles)
- Lagrangian formalism
- Relativistic fields
- Hamiltonian formalism
- Lagrangian formalism (Least action principle)
- Relativistic fields revisited
- Noether's theorem and Symmetries
- Review of Quantum mechanics
- Second Quantization
- Field Operators
- Fock Space and vaccum Energy
- Quantization of Bosons and Fermions
- Examples
- Free Fermi gas
- Propagators and perturbations
- Relativistic quantum field theory
- Feynman Propagator
- Review of Statistical Mechanics (Partition Function)
- Feynman Path Integral
- Diagrammatic Field Theory (Wick's Theorem)
- Wick's Theorem (Continuation)
- Diagrammatic Perturbation Theory
- Green's Function and Correlation Function
- Feynman Diagrams
- Phase Transition and Landau Theory
- Failure of Landau's Theory
- Scale Invariance
- Renormalization group - preliminary
- RG Steps
- Perturbative Calculations
- RG fixed points
- Relevant and Irrelevant variables
- Behavior Near critical points
- Computing Critical Exponents
- Running coupling const: phi^4 theory
- Charge and mass renormalization: QED & QCD
- Breaking a Continuous Symmetry (Goldstone Mode)
- Covariant Electrodynamics (Gauge Interactions)
- Higgs Mechanism
- Introduction to Non-Equilibrium Field Theory (Langevin Equation)
- Fluctuation Dissipation Theorem
- Kolmogorov's Theory of Turbulence
- Equilibrium and Non equilibrium Solution of Navier Stokes
- Energy Flux in Navier Stokes Equation
- RG shell model
- RG shell model contd
- Renormalization of the coupling constant for the shell model
- Flux Computation for the Shell Model of Turbulence
- Renormalization Group Analysis of Navier Stokes Equation
- Flux Computation for the Navier Stokes Equation
- Functional Form of a Dynamical Equation
- Surface Growth Phenomena : Introduction
- Surface Growth Phenomena : EW equation
- Surface Growth Phenomena : KPZ equation
- Surface Growth Phenomena : KPZ continued
- RG prodecure for KPZ equation
- Noise Renormalization
- Fixed Point Solution
- Weak Turbulence Theory using examples
- Weak Turbulence Applications (Rotating Turbulence, Internal and Surface Gravity Waves)
- Nonlinear Schrodinger Equation
- Field Theory of Passive Scalar Turbulence
- Course Summary