Quantum Field Theory II

U. Tokyo undergraduate/graduate course, 2016 autumn semester

Objectives

The second course on Quantum Field Theory.
Tree-level computations and path integral are the two major materials to be covered in this course. We will also discuss bound states, low-energy effective theory and unitarity along the way.

Prerequisite: equivalent of QM III (2nd quantization), QFT I (free field quantization) and Quantum Optics (photon quantization, atomic transition)

Hours and Rooms: Mondays 14:55--16:40 at room 207, Rigakubu 1 Goukan (Hongo Campus)
Office hour:           Mondays 16:40--17:40 at room 207, or 903, the same as above.

Instructor: Taizan Watari,           Kavli IPMU, Kashiwa Campus
TA:           Nozomu Kobayashi,   Kavli IPMU, Kashiwa campus

Language: primarily in Eniglish, with occasional summary provided in Japanese. Questions in Japanese are also welcome during the class.

Announcement:
                (1) All the homework problems will be posted here.
                (2) Note the change in the language policy (since Oct. 3).
                (4) Homework problems E-1, E-2, ....., E-6 are now posted below. (Nov. 27)
                (5) Homework submission deadline: Jan 30 (Mon), until the end of the office hour.

Lecture Notes and Homework Problems: (see general instruction on homework problems)

Sep. 26: note-01 hw-01 introduction, S-matrix, decay rate, cross section
                                          [4.5, [W-I 3.1, 3.2]]
Oct. 03: note-02 hw-02 LSZ formula, spectral representation
                                          [4.2--4.4, 4.6--4.8, 7.1, 7.2, [W-I 4.3, 10.7]]
Oct. 17: note-03 ----- Feynman rule, loop expansion // vector field propagator, e+e- to mu+mu-
                                          [3.2, 3.3, 3.5, 4.3, 4.4, 4.6--4.8, [W-I 6., 8.], 5.1]
                                          [For section 2.4 of the lecture note, see [LB 2.3, 2.5, 3.3], [K 2.1--2.7], [AS 7., 11.] and hw E-2, E-3]
Oct. 24: note-04 hw-04 e+e- to mu+mu-: unpolarized (high energy, threshold), polarized
                                          [5.1--5.3]
Oct. 31: note-05 hw-05 crossing symmetry, t-channel 2to2, non-relativistic limit, Mott scattering, LS coupling
                                          [5.4]
Nov. 07: note-06 ----- Compton/Thomson scattering // Bethe-Salpeter equation
                                          [5.5, [Ni 3.4, 3.5], [LL4 125], [T 10]]
Nov. 14: note-07 hw-07 Bethe-Salpeter equation, fine structure, hyperfine structure, Lamb shift
                                          [[LL4 125], [T 10], [LL4 33, 34], [Ni 1.10], [LL4 123], 7.5, Wikipedia]
Nov. 21: note-08 hw-08 atomic transition // partial wave unitarity
                                          [??, [W-I 3.6--3.8]]
Nov. 28: note-09 ----- optical theorem // low-energy effective theory //
                                          [7.3]
Dec. 05: note-10 ----- path integral formulation of quantum mechanics
                                          [[FH 3, 8], [Na 2.1], [AS 3.2], 9.1]
Dec. 12: note-11 hw-11 path integral for a 2-state (fermionic) system, and for QFTs
                                          [[Na 2.3; 2.2], [AS 4.2], 9.5, 9.2, 9.3, [LB 5.1, 6.1]]
Dec. 19: note-12 ----- free energy, effective action
                                          [11.3-5, 16.6, [W-II 16.1-3, 21.6]]
Dec. 26: note-13 hw-13 thermal field theory (imaginary time formalism)
                                          [8, 9.2, 9.5, [LB 2.1, 2.6, 3.1]]
Jan. 16: note-14 hw-14 coarse graining, real time (Keldysh) formalism //
                                          [[LB, K (see Refs. for the week 3)], [hw E-2]]
Jan. 23: note-15 ----- 1-loop computation (anomalous magnetic moment) //
                                          [6.2, 6.3]
Jan. 30: note-16 ----- a bonus track: Borel resummation
                                          [[W-II 20.7], [AS 5.1], arXiv:1403.1277]

Advanced homework problems: D-1, D-2, D-3 and E-1, ..., E-6.

Materials that this course did not cover pdf

numbers in [     ] are the relevant sections in textbooks and references. When the textbooks or references are not specified, that is [PS] below.

Textbooks and References:

This course is not based on a specific textbook. I often refer to the following textbooks, though, when I prepare for lectures:

[PS] M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory,
[LL4] V. B. Berestetskii, E. M. Lifshitz and L. P. Pitaevskii, Quantum Electrodynamics,
[W-I, II] S. Weinberg, The Quantum Theory of Fields volume I and II.

[LB] M. Le Bellac, Thermal Field Theory,
[K] A. Kamenev, Field Theory of Non-Equilibrium Systems,
[AS] A. Altland and B. Simons, Condensed Matter Field Theory,
[T] Yasushi Takahashi, 物性研究者のための場の量子論 II,
[Ni] Kazuhiko Nishijima, 相対論的量子力学,
[FH] R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals,
[Na] Naoto Nagaosa, Quantum Field Theory in Condensed Matter Physics (物性論における場の量子論),

Plan of the progress
1. introduction
2. S-matrix etc., loop expansion: [2 weeks]
3. tree-level scattering processes: [3 weeks]
4. bound states: [2 weeks]
5. unitarity: [1 week]
6. low-energy effective theory: [1 week]
7. path integral: [5 weeks]
8. introduction to 1-loop computation: [1 week]

Grading Scheme: Letter grading [ excellent, good, OK or fail ] based on reports.

All the homework problems will be posted here.
Each homework problem is in either one of categories A, B, C, D and E, and you will pass (excellent, good or OK) if

1 x #[A] + 1.5 x #[B] + 2 x #[C] + 4 x #[D] + 9 x #[E] is 9 or larger.

Submission: QFT II report box at the 2F Physics Administration Office.
                When submitting your report to a post at the door of the admin. office, remember to write "QFT2" at the head of your report.
Electronic submission: to the e-mail address announced in the classroom. Make sure that you receive an automatic reply.
                Attachment files are not opened, so this option is only for Category [A] problems where several lines of sentences are enough.
                I ask that the Subject line is written as "Date of a relevant lecture" "student ID" [example: Sep 26 ss921456]
Submission deadline: Jan 30 (Mon), until the end of the office hour.