AQM: Fall 2018

Organization

• Updates.
  • Problem set 1 is up: due August 20. Extended to August 24.
  • Problem set 2 is up: due September 03. Extended to Sep 8.
  • Problem set 3 is up: due September 10. Extended to Sep 15.
  • Problem set 4 is up: due September 30.
  • Problem set 5 is up: due October 15. Extended to Oct 22.
  • Problem set 6 is up: due Oct 30.
  • Problem set 7 is up: due Dec 7.
  • Some notes on Feynman diagrams are here FeynmanRules
• Class schedule.
  1. Monday 0945-1115 in A304. Changed to Monday 4:05 to 5:25 in A269.
  2. Wednesday 0945-1115 in A304. Changed to Wednesday 4:05 to 5:25 in A269.
  Please let me know if there are any conflicts as soon as as possible.
• Suman Kundu is your TA ( kundusuman1994 @ gmail ). You can give your problem set solutions directly to him. suman's office is in D429.
• Problem sets.
  1. Problem set 1 due 20 August 2018.
  2. Problem set 2 due 03 September 2018.
  3. Problem set 3 due 10 September 2018.
  4. Problem set 4 due 30 September 2018.
  5. Problem set 5 due 15 October 2018.
  6. Problem set 6 due 30 October 2018.
  7. Problem set 6 due 07 December 2018.
• Tests.
  1. Mid term examination
  2. Final presentation
• References
  1. (Path integrals, Many body theory) Quantum Field Theory Lowell Brown
  2. (Path integrals) Online notes by Hitoshi Murayama Hitoshi Murayama
  3. (Scattering Theory) Advanced quantum mechanics J. J. Sakurai
  4. (Scattering Theory) Advanced quantum theory P. Roman
• Prerequisites
  1. Quantum Mechanics II
• Curriculum.
  1. August 6, 2018. The path integral formulation of Quantum Mechanics. (Chapter 1, Lowell Brown; Online notes by Hitoshi Murayama)
  2. August 8, 2018. Gaussian integrals. Path integral for the harmonic oscillator. (Chapter 1, Lowell Brown; Online notes by Hitoshi Murayama)
  3. August 13, 2018. Path integral for the harmonic oscillator with discretized time. (Chapter 1, Lowell Brown; Online notes by Hitoshi Murayama)
  4. August 20, 2018. Feldholm determinants. Path integral for the harmonic oscillator in continuous time. (Chapter 1, Lowell Brown; Online notes by Hitoshi Murayama)
  5. August 27, 2018. Long time behaviour of path integrals. Correlation functions. Feynman rules. (Chapter 6, 7 Srednicki QFT book. Available online.)
  6. August 29, 2018. Feynman rules contd. (Chapter 10 Srednicki QFT book. Available online.) Imaginary time and statistical mechanics (Sections 6.1, 6 .2 and 8.1, 8.2 in Path integrals notes by Wipf. Available Online.).
  7. September 5, 2018. Quick review of the basics of time independent scattering Theory. Cross-section definition. Green's functions for scattering. Messiah Chapter X, Sections 1-6. (For people familiar with Sakurai, please revise Chapter 7 from Sakurai.)
  8. September 10, 2018. First born approximation. Quick review of the partial waves formalism for central potential scattering. (Paul Roman, Sec. 3.2, 3.3, 3.4)
  9. September 12, 2018. Partial wave analysis in detail. (Quantum Collision Theory, Charles Jochain, Chapter 4)
  10. September 17, 2018. Scattering phase shifts in the low and high momentum regimes. Resonances. (Quantum Collision Theory, Charles Jochain, Chapter 4)
  11. September 19, 2018. Lippmann-Schwinger equation. In-Out states in the time independent formalism. (Secs. 4.1, 4.2, Paul Roman). Scattering theory in the time dependent fomalism (Secs. 3.5, 4.3, Paul Roman)
  12. September 24, 2018. Scattering theory in the time dependent fomalism (Secs. 3.5, 4.3, Paul Roman)
  13. September 26, 2018. Scattering theory in the time dependent fomalism and Feynman rules (Secs. 3.5, 4.3, Paul Roman)
  14. September 30, 2018. Mid Sem exam.
  15. October 1, 2018. Many body theory (Chapter 2, Lowell Brown)
  16. October 3, 2018. Coherent state path integrals for Bosons (Chapter 2, Lowell Brown and Chapter 1, Lowell Brown)
  17. October 8, 2018. Coherent state path integrals for Bosons completed. (Chapter 2, Lowell Brown and Chapter 1, Lowell Brown) Grassman numbers and the path integrals for many fermion systems (Chapter 2, Lowell Brown)
  18. October 10, 2018. Path integrals for fermions continued. Definition of integration and differentiation over Grassman numbers. Defition and calculation of correlation functions of time ordered Grassman fields. Feynman rules. Scattering of identical particles: exchange symmetry. (Chapter 2, Lowell Brown)
  19. October 15, 2018. Many body statistical physics. Euclidean rotation. Periodic boundary conditions for bosons and antiperiodic boundary conditions for fermions (Chapter 2, Lowell Brown)
  20. October 17, 2018. Many body statistical physics. Non-interacting Fermi and Bose gases. The partition function. (Chapter 2, Lowell Brown)
  21. October 22, 2018. Symmetries in quantum mechanics. Wigner's theorem on the representations of symmetries. (Weinberg, QFT Foundations, Chapter 2)
  22. October 24, 2018. Symmetries and their representations. Definition of projective representations. Introduction to Lie groups and Lie algebra. (For a nice introduction to SO(3) and SU(2) see Chapter 4 of Goldstein, Classical Mechanics. For a nice introduction to discrete groups see Georgi, Lie Algebras in Particle Physics Chapter 1. For the definition of Lie Algebras see Chapter 2 of Georgi.)
  23. October 29, 2018. Projective representations and central charges. Lorentz group and the Lie Algebra. (Weinberg Chapter 2.)
  24. October 31, 2018. Poincare group. Absence of central charges in the poincare group. SL(2, C) versus SO(3, 1). Topology of SL(2, C) versus SO(3, 1). (Weinberg Chapter 2.) Contrast with the group of Galilean transformations. (Lowell Brown Chapter 2, Problem 1.)
  25. November 12, 2018. Unitary representations of the Poincare group. Absence of the central charge in the Poincare algebra. Eigenstates of momentum. Little group: 6 cases. Little group for a massive physical particle. (Weinberg Chapter 2.)
  26. November 14, 2018. Little group for a massless particle. Representations of ISO(2). (Weinberg Chapter 2)
  27. November 19, 2018. Classical (rather than quantum) representations of the Poincare group. Classical field theory. Scalar field theory. The lagrangian and the path integral for the scalar field. Spectrum of the scalar field theory. Poincare representation. Non-unitary representations of SL(2, C). Lie algebra. Writing SL(2, C) as SU(2)xSU(2). (Srednicki Chapter 33)
  28. November 26, 2018. Spinor representations of SL(2, C). Weyl lagrangian. Dirac lagrangian. (Srednicki Chapter 33, 34)
  29. November 28, 2018. Dirac lagrangian. (Srednicki Chapter 33, 34). Solutions of the Dirac equation. (Srednicki Chapter 38, Peskin Chapter 2).
• Grading scheme.
  1. Problem sets: 50%
  2. Mid term examination: 20-30% September 30.
  3. Final examination: ?%