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

ABOUT THE COURSE: Quantum field theory and statistical field theory have been employed to explain many difficult natural phenomena successfully, and they are must-learn tools for particle, condensed matter, and statistical physicists. These tools have also been useful for modelling nonequilibrium systems, such as KPZ equation, time-dependent Ginzburg-Landau equation, and turbulence. In this course, we will cover various facets of field theory in a single canvas so as to compare and contrast important paradigms. This course will focus on breadth of field theory. I believe that such perspectives will enrich the perspectives of students.INTENDED AUDIENCE: Masters and PhD students, as well as advanced UG students of PhysicsPREREQUISITES: Quantum Mech, Mathematical Methods, Statistical Physics. Good background in mathematics required.

Week 1:
Module 1 : Green’s function
Module 2 : Lagrangian & Hamiltonian for fields
Module 3 : Functional integrals
Module 4 : Generic integrals
Week 2:
Module 1 : QFT1: Second quantization
Module 2 : Symmetries
Module 3 : Noether’s theorem
Week 3:
Module 1 : Complex scalar field
Module 2 : Propagators and perturbation theory
Module 3 : Feynman diagrams
Week 4:
Module 1 : Statistical field theory: Intro to statmech
Module 2 : Path integrals and partition function
Module 3 : Landau’s theory of phase transition
Week 5:Module 1 : Mean field theory
Module 2 : Wilson theory of phase transition; Fluctuations
Module 3 : Renormalization groups
Week 6:
Module 1 : Renormalization groups
Module 2 : Equilibrium vs. nonequilibrium
Module 3 : Energy transfers
Week 7:
Module 1 : QFT2: Intro to gauge theory
Module 2 : Intro to QED
Module 3 : Mass and charge renormalization
Week 8:
Module 1 : Higgs mechanism
Module 2 : Higgs mechanism
Module 3 : Asymptotic freedom
Week 9:
Module 1 : Classical field theory
Module 2 : Nonequilibrium behaviour
Module 3 : Dynamical critical phenomena
Week 10:
Module 1 : KPZ equation
Module 2 : Time-dependent Ginzburg-Landau eqn.
Module 3 : Field theory of hydrodynamic Turbulence
Week 11:
Module 1 : Field theory of hydrodynamic Turbulence
Module 2 : Field theory of Euler Turbulence
Module 3 : Scalar turbulence
Week 12:
Module 1 : Magnetohydrodynamic turbulence
Module 2 : Comparation between QFT, SFT and classical field theory
Module 3 : Summary