qftforgiftedamateur     qftinanuttshell    introduction-to-many-body-physics-coleman

go to site Course outline: The outline can be downloaded here.

http://candacenkoth.com/?q=how-to-buy-viagra-on-craigslist Class timings: 10:30 to 11:45 am, Monday and Wednesday, Room: 202  SSE Complex.

http://candacenkoth.com/?q=uk-buy-viagra Marking scheme: Homeworks 40%, Midterm 30%, Final 30%

Pre-mid term

sdTo access the video recording, click on the numbered links below.

Introduction to Quantum Field Theory: Prerequisites

1: Overview and Special Relativity (Lecture 1)

  • Overview
  • 4-Vectors, Minkowski space
  • Lorentz transformation, Lorentz boost
  • Natural units vs relativistic units
  • Space time diagrams, Simultaneity
  • Lorentz invariants

2: Special Relativity and Classical Mechanics (Lecture 2)

  • Special relativity: 4-velocity
  • Mechanics of relativistic particles
  • Final momentum from langrangian
  • Energy of the system: Hamiltonian
  • Minkowski tensor and inner product

3: Classical Field Theory (Lecture 3)

  • Simple concept of field
  • Example of a single particle
  • Non-relativistic particle equation
  • Basic principles of field theory
  • Klein-Gordon equation
  • Solution to Klein-Gordon equation
  • Particles inside two interacting scalar fields

Homework 1: Hw1 (pdf) (Due date: 6 February, 2018 10:00 am) Solution: Solution 1 (pdf)

4: Lagrangian Formulation of Electromagnetism (Lecture 4)

Homework 2: HW2 (pdf) (Due date: 15 February, 2018 04:00 pm) Solution: Solution 2 (pdf)

5: Electromagnetic Field Tensors (Lecture 5)

  • Electric field components
  • EM field tensor
  • Maxwell’s equations (homogeneous and in homogeneous)
  • Locality principle
  • Lorentz co-variant form of in homogeneous Maxwell’s equations
  • Gauge invariance

Homework 3: HW3 (pdf) (Due date: 19 February, 2018 04:00 pm) Solution: Solution 3 (pdf)


Introduction to Quantum Field Theory: Second Quantization

6: Noether’s Theorem, Second Quantization (Lecture 6)

  • Derivation, Noether’s current, Noether’s momentum
  • Energy momentum tensor
  • Uncoupled and Coupled harmonic oscillators
  • Second quantization

7: Second Quantization continued: Quantization of Operators (Lecture 7)

  • Occupation number
  • Continuum limit
  • Field operators
  • Second quantization of single particle operators
  • Examples

Homework 4: HW4 (pdf) (Due date: 26 February, 2018 04:00 pm) Solution: Solution 4 (pdf)

8: Examples of Second Quantization (Lecture 8)

  • Second quantized form of Hamiltonian (in position and momentum space)
  • Interaction (2 – particles) – Feynman diagram
  • Magnetic interactions (String operators, Jordan-Wigner transformations)
  • Further examples – Magnons, Tight binding model, Hubbard model.

Homework 5: HW5 (pdf) (Due date: 5 March, 2018 04:00 pm) Solution: Solution 5 (pdf)


Introduction to Quantum Field Theory: Canonical Quantization

9: Scalar Field – Canonical Quantization (Lecture 9)

  • Time evolution
  • Heisenberg picture
  • Canonical momentum
  • Hamiltonian density
  • Field in terms of creation and annihilation operator, Mode expansion
  • Hamiltonian
  • Normal ordering
  • Positive and negative energies

10: Complex Scalar Field – Canonical Quantization (Lecture 10)

  • Canonical quantization of complex scalar field
  • Klein-Gordon equation for non-relativistic regime
  • Canonical quantization of truncate the complex scalar field

Homework 6: HW6 (pdf) (Due date: 13 March, 2018 10:00 am) Solution: Solution 6 (pdf)

11: Multicomponent Quantum Field – Canonical Quantization (Lecture 11)

  • 3-component field (electromagnetic field) canonical quantization
  • Fictitious particle – Massive photon canonical quantization
  • Polarization
  • Internal symmetry

Midterm exam: midterm + solution (pdf) (13 March 2018)


Post-mid term

Introduction to Quantum Field Theory: Gauge Transformation

12: Gauge Transformations (Lecture 12)

  • Introduction
  • Gauge transformation of classical complex massive fields
  • Electromagnetism as a U(1) gauge theory
  • Choice of gauge
  • Lorenz gauge
  • Coulomb gauge

Homework 7: HW7 (pdf) (Due date: 2 April, 2018 10:00 am) Solution: Solution 7 (pdf)


Introduction to Quantum Field Theory: Propagatorsfeynman_diagrams_on_yellow_background_poster_by_muonrayartlab-d9u5g68

13: Propagators (Lecture 13)

  • Introduction
  • Green’s functions
  • Propagators
  • Free particle
  • Green’s function in the Fourier domain

14: Feynman Propagators (Lecture 14)

  • Space-time translations
  • Transformation of quantum fields
  • Feynman propagator
  • Interacting system
  • Free propagator

15: Interaction Propagators (Lecture 15)

  • Interaction picture
  • Scattering matrix (S – matrix)
  • Wick’s time ordering

Homework 8: HW8 (pdf) (Due date: 10 April, 2018 10:00 am) Solution: Solution 8 (pdf)

16: Computing the Terms in the Dyson Expansion of Scattering matrix (Part A) (Lecture 16)

  • Zeroth order term
  • Wick’s theorem
  • Feynman diagrams

17: Computing the Terms in the Dyson Expansion of Scattering matrix (Part B) (Lecture 17)

  • Phi-4 theory
  • Examples (Bosonic fields)
  • Yukawa’s theory

18: Dirac Equation – Quantum Field Theory (Lecture 18)

  • Dirac equation
  • Representing gamma (or Dirac) matrices
  • Alternative way of expressing Dirac equation
  • Chirality operator
  • Dispersion relation for massive Dirac particles
  • Non relativistic version of Dirac equation – Pauli equation

Homework 9: HW9 (pdf) (Due date: 19 April, 2018 10:00 am)


Introduction to Quantum Field Theory: Spinor Fields

19: Transformations (Lecture 19)

  • Continuous transformations: Spacetime, Rotation
  • Representation e.g, Spin 1 particle
  • Quantum fields
  • Scalar fields and Vector fields
  • Lorentz boost
  • Discrete transformation: Charge conjugation, Parity operation, Time reversal operation
  • Time reversal symmetric (TRS) system