QFT1: Spring 2014

Organization

• Updates.
  • The final exam is on Saturday, May 24
  • Problem set 9 is up: due May 23
  • Problem set 8 is up: due May 11
  • Problem set 7 is up: due April 21
  • Problem set 6 is up: due April 14
  • Mid term exam 29th March from 2pm to 5 pm
  • Tutorial 28th March to discuss problem sets and common errors
  • Class 27th March at 4pm in the DTP seminar room
  • Problem set 5 extension till March 28, 7pm (Sharp cutoff)
  • Problem set 5 is up: due March 21
  • Tomorrow I will try to discuss some things about in/out states, so it won't be purely a tutorial. The discussion will be done in the context of Problem 3 in Problem set 5.
  • I'm thinking of holding a mid-term examination either on 28th March or 29th March. I'll look for some feedback before I decide
  • There will be no class next week on 25 and 27 because of the admissions. There will however be a problem set 4
  • To compensate, instead of having a tutorial on the 28th of February, we will have a class
  • Due date for Problem set 3 is extended to 28 Feb. A typo in Problem 2c corrected ($p^0(i+i\epsilon)\rightarrow p^0(1+i\epsilon)$)
  • No quiz on Feb 21, 2014
  • Problem set 4 is online. It is due on the 7th of March
  • For Problem set 3, Problem 2e (last part of problem 2) is cancelled. A simple relation can only be obtained for space-like separations, not time-like separations
• Class schedule.
  1. Tuesday 1430-1600 in A304
  2. Thursday 1430-1600 in A269
  3. Friday 1730-1900 in A304 (tutorial)
  Please let me know if there are any conflicts as soon as as possible.
• Mangesh Mandlik from the DTP has kindly agreed to TA the class. His office is located in D 429 (graduate students room) and his email id is mangesh @ theory. You can give your problem set solutions directly to him.
• Problem sets (roughly 1 per week).
  1. Problem set 1 due 11 Feb 2014.
  2. Problem set 2 due 18 Feb 2014.
  3. Problem set 3 due 26 Feb 2014 [Extended to 28 Feb]
  4. Problem set 4 due 7 Mar 2014.
  5. Problem set 5 due 21 Mar 2014.
  6. Problem set 6 due 14 Apr 2014.
  7. Problem set 7 due 21 Apr 2014.
  8. Problem set 8 due 11 May 2014.
  9. Problem set 9 due 23 May 2014.
• Tests.
  1. There will be no quiz on Feb 21 2014
  2. Mid term examination
  3. Final examination
• References
  1. An introduction to Quantum Field Theory Michael E. Peskin and Daniel V. Schroeder
  2. Quantum Field Theory Lowell S. Brown
  3. Quantum Field Theory Mark Srednicki. Rough draft of the book is available online
• Prerequisites
  1. Advanced Quantum Mechanics
  2. Classical mechanics
• Curriculum.
  1. Feb 4, 2014. Rewriting many particle quantum mechanics in terms of quantum fields. Creation and annihilation operators. Natural units. (Brown Chapter 2, Srednicki Chapter 1)
  2. Feb 6, 2014. Heisenberg picture. Many particle quantum mechanics starting from a lagrangian view point. Equal time commutation and anti-commutation relations. Momentum operator as a generator of spatial translations and Hamiltonian as a generator of time translations. Refresher on the principle of least action, Lagrangians, classical field theories (Brown Chapter 2, Srednicki Chapter 1)
  3. Feb 11, 2014. Refresher on special relativity and Einstein's index notation. Lagrangian for a scalar field. Hamiltonian. Poisson brackets. Quantization of the non-interacting, real, scalar field. (Srednicki Chapter 2, 3, Peskin Chapter 2)
  4. Feb 13, 2014. Quantization of the scalar field. Creation and annihilation operators. Normal ordering. On-shell momenta. Lorentz invariant measure for on-shell momenta. Lorentz transformation properties of fields and operators. Multiparticle states. Operators, generators of symmetry transformations, Noether's theorem. The stress energy tensor (Srednicki Chapter 3, 22, Peskin Chapter 2)
  5. Feb 18, 2014. Correlation functions. Causality. Causality in non-relativistic theories. Retarded propagator. Time ordered correlation functions. Feynman propagator. (Peskin Chapter 2)
  6. Feb 20, 2014. Introduction to interacting theories. $phi^4$ theory. Comparison between Heisenberg, Schroedinger and interaction pictures. Time evolution operator in the interaction picture. Correlation functions in the interaction picture. Asymptotic vacuum state. Time ordering. Wick's theorem (Peskin Chapter 4)
  7. Feb 28, 2014. Wick's theorem. Introduction to Feynman diagrams. (Peskin Chapter 4, Srednicki Chapter 9)
  8. Mar 4, 2014. (Thanks to Saumen for taking this class.) Details about position space Feynman rules. Symmetry factors. (Peskin Chapter 4, Srednicki Chapter 9)
  9. March 11, 2014. Momentum space Feynman rules. Wavepackets: broadening and motion. In/Out states. Scattering processes. LSZ reduction. (Peskin Chapter 4, Srednicki Chapter 5, Peskin 7.1, 7.2)
  10. March 13, 2014. LSZ reduction. Relation between correlation functions and scattering matrix elements. $T$-matrix. Invariant matrix element $i {\cal{M}}$. Relation between the scattering matrix and decay rates $\Gamma$. Relation between $i{\cal{M}}$ and differential cross-sections $\sigma$ (Peskin Chapter 4, Srednicki Chapter 5, Srednicki Chapter 11, Weinberg Section 3.4)
  11. March 14, 2014. S-matrix. In/Out states. External fields. (Peskin Chapter 1 and 4)
  12. March 18, 2014. Transformation properties of $i{\cal{M}}$, $\sigma$ and $\Gamma$. LSZ reduction. Wavefunction re-normalization. ( Srednicki Chapter 5)
  13. March 18, 2014. Fun with Feynman diagrams
  14. March 27, 2014. Noether's theorem redux. Feynman rules for the complex scalar field theory.
  15. March 28, 2014. Review of problem sets. General discussion.
  16. March 29, 2014. Mid term exam.
  17. April 1, 2014. Introduction to counter-terms for interacting field theories. (Srednicki Ch 9 in canonical language.)
  18. April 3, 2014. Feynman rules for scattering processes and lowest order scattering with counter-terms. Connecting scattering amplitudes to cross-sections and decay rates.
  19. April 4, 2014. Review of the mid term examination.
  20. April 8, 2014 to April 24, 2014. Renormalized perturbation theory for scalar theories.
  21. April 24, 2014 to May 20, 2014. Spin 1/2.
• Grading scheme.
  1. Problem sets: 50%
  2. Mid term examination: 20%
  3. Final examination: 30%