Physics 7640 Lecture Plan

Last modified 25 March 2009

Contents

• Week 1 , Week 2 , Week 3 , Week 4
• Week 5 , Week 6 , Week 7 , Week 8
• Week 9 , Week 10 , Week 11 , Week 12 ,
• Week 13 , Week 14 , Week 15 , Week 16 ,

Introduction to Quantum Field Theory

• Review of Quantum Mechanics
  • Single-particle quantum mechanics
  • Simple harmonic oscillator
  • Coherent states
  • Time-dependent perturbation theory
  • Time evolution and Interaction Picture
  • Primitive Feynman diagrams
  • Scattering theory, transition rates, cross section
  • Many Body Quantum Mechanics
  • Fock space for fermions and bosons
• Second quantization
  • Phonons
  • Relativistic scalar field
  • Feynman diagrams and phi⁴ theory
  • Cross sections in phi³ theory
  • Renormalization in phi⁴ theory
• Electromagnetic field
  • Lagrangian approach to Maxwell's equations
  • Quantization of the EM field
  • Gauge choices
• Electron/positron field
  • Dirac equation
  • Quantization of the fermion field
  • Normal ordering
  • Dirac sea and Fermi sea
• Quantum electrodynamics
  • QED Lagrangian
  • Feynman rules
  • Simple scattering processes
  • Gauge choices
  • Renormalization
  • Ward-Takahashi identity
  • Running coupling and beta function
  • Test of QED: Lamb shift and g-2
• Radiation in atomic systems
  • Interaction of EM field with atoms
  • Thermal equilibrium between atoms and radiation
  • Elementary theory of lasers
  • Coherence in light
  • Intensity correlations: Hanbury Brown - Twiss
• Fermi gas and Fermi liquid
  • Single particle density
  • Debye-Huckel screening
• Spontaneous symmetry breaking
  • Plasmon oscillations
  • Bose-Einstein condensates
  • BCS theory of superconductivity
  • Electroweak symmetry breaking

Physics 7640 Lecture Plan

• Week 1

  1-12-09 Introduction. Review of quantum mechanics 1,2
  • Course organization (slides)
  • Review of QM 1: wave equation (slides)
  • Review of QM 2: Dirac notation. Matrix quantum mechanics. (slides)
  
  1-14-09 Review of quantum mechanics 3,4
  • Review of QM 3: Simple harmonic oscillator. (slides)
  • Review of QM 4: Coherent states (slides)
  
  

• Week 2

  1-19-09 (Martin Luther King, Jr. Day)
  
  1-21-09 (Last day to drop classes)
  
  1-21-09 Review of quantum mechanics 5,6,7
  • Review of QM 5: Time-dependent perturbation theory: Interaction picture, etc (slides)
  • Review of QM 6: Primitive Feynman diagrams (slides)
  • Stationary state perturbation theory. Gell-Mann-Low Theorem (slides)
  
  
  1-23-09 Review of Quantum Mechanics 8,9
  • Scattering Theory: Lippmann-Schwinger equation (slides)
  • S-Matrix, T-Matrix and Scattering amplitude (slides)
  
  

• Week 3

  1-26-09 (Instructor out of town)
  
  1-28-09 (Instructor out of town)
  
  1-30-09 Review of Quantum Mechanics 10
  • Transition Rates, Cross Sections, Optical Theorem (slides)
  
  

• Week 4

  2-02-09 (Instructor absent)
  
  2-04-09 Many Body Physics 1,2
  • Fock Space for Bosons (slides)
  • Fock Space for Fermions, Noninteracting (slides)
  
  2-06-09 Many Body Physics 3,4,5
  • Fock Space for Fermions, Interactions (slides)
  • Fock Space for Bosons, Interactions (not covered in class) (scanned notes)
  • Hamiltonian in terms of fields for bosons and fermions. (slides)
  
  

• Week 5

  2-09-09 Fields and Lagrangians
  • Redefining the vacuum. (slides)
  • Review of Lagrangian Mechanics (slides)
  • Canonical Quantization from the Lagrangian (slides)
  
  2-11-09 Lagrangian Approach. Phonons
  • Phonons in One Dimension (slides)
  
  

• Week 6

  2-16-09 (President's Day)
  
  2-18-09 Phonons
  • Phonons in Three Dimensions (slides)
  • Relativistic scalar field 1 (1D case) (slides)
  
  

• Week 7

  2-23-09 Relativistic Scalar Field; Perturbation Theory
  • Relativistic scalar field 2 (3D case) (slides)
  • Feynman Propagator and Wick's Theorem (slides)
  
  2-25-09 Feynman Diagrams and Rules for Phi 4 Field Theory
  • Feynman Diagrams (slides)
  • Feynman Rules (slides)

• Week 8

  3-02-09 (Instructor absent)
  
  3-04-09 Applications of Feynman Diagrams and Cross Sections
  • Cross Sections in Phi 3 Field Theory (slides)
  
  3-06-09 Renormalization
  • Ultraviolet Divergences (slides)
  • Renomalization in Phi 4 Field Theory (slides)
  
  

• Week 9

  3-09-09 (Instructor out of town)
  
  3-11-09 Renormalization and Photons
  • The renormalized Lagrangian in Phi 4 Theory (slides)
  • Photons from the Lagrangian approach to Maxwell's equations (slides)
  
  
  

• Week 10

  3-16-09 (UU Spring Break)
  
  3-18-09 (UU Spring Break)
  
  

• Week 11

  3-23-09 The Free Dirac Field
  • Plane Wave Solution of the Dirac Equation (slides)
  
  3-25-09 Quantum Electrodynamics
  • QED Lagrangian, Feynman rules, electron-positron annihilation (slides)
  
  
  

• Week 12

  3-30-09 Quantum Electrodynamics (slides)
  • Moller scattering.
  • Coulomb vs Feynman gauge.
  • Crossing symmetry
  • Divergences
  
  4-01-09 Quantum Electrodynamics (slides)
  • Renormalization constants Z1, Z2, and Z3
  • Renormalized QED Lagrangian
  • Renormalization procedure
  • Ward-Takahashi Identity
  
  

• Week 13

  4-06-09 Running Coupling and Tests of QED (slides)
  • Running Coupling in QED
  • Beta function
  • Lamb shift
  • g-2 for the electron
  
  4-08-09 Radiation in Atomic Systems (slides)
  • Field theory for atoms in the presence of Radiation
  • Spontaneous and stimulated emission, absorption.
  • Planck radiation formula
  • Thermal equilibrium between atoms and radiation
  
  

• Week 14

  4-13-09 Coherence in Light (slides)
  • Black body vs coherent sources
  • Amplitude coherence / correlations
  • Intensity correlations: Hanbury Brown - Twiss
  
  4-15-09 Fermi gas and Fermi liquid (slides)
  • Single particle density
  • Debye-Huckel screening via bubble diagrams
  • Plasmon oscillations
  • Landau damping
  
  

• Week 15

  4-20-09 Spontaneous Symmtry Breaking (slides)
  • Spontaneous symmetry breaking
  
  4-22-09 Bose-Einstein condensates (slides)
  • Bose-Einstein condensates
  • Bogoliubov transformation
  
  

• Week 16

  4-27-09 Superconductivity (slides)
  • Overview of London Theory
  • Ginzburg-Landau Theory
  
  4-29-09 Superconductivity (slides)
  • Anderson-Higgs mechanism
  • BCS Theory Simplified
  
  

• Week 18

  5-06-09 Take-home final exam due at 4 PM 212 INSCC.
  

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