Quantum Field Theory II (QFT)

U. Tokyo undergraduate/graduate course, 2020 autumn semester

This course corresponds
to "Quantum Field Theory II" (code: 0515071) in the UTokyo Course Catalogue for undergraduate students, and
to "Quantum Field Theory" (code: 35603-0119) for graduate students.

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). We assume that the students in the classroom are familiar with free field quantization (incl. derivation of the propagator (Green function)) from Week 3 in this semester.

Hours and Rooms: Mondays 14:55--16:40 at room 206, Rigakubu 1 Goukan (Hongo Campus) on Zoom. See U Tokyo ITC-LMS for the URL.
                                  Week 2~ : 14:55--16:40 (1hr45min)
                                  (Graduate) School of Science's official time table is 15:10--16:40 this autumn; yes, I know that.
                                  But the (Graduate) School of Science also says that a bit of flexibility is tolerated, if that is for the benefits of the students.
                                  The office hour can be exploited for necessary compensation.
Office hour:           Mondays 16:40--17:40.

Instructor: Taizan Watari,           Kavli IPMU, Kashiwa Campus
TA:           Weiguang Cao,           Kavli IPMU, Kashiwa campus

Language: explanations in Eniglish. Questions in Japanese are also welcome during the class.

Announcement:
                (2) All the homework problems will be posted either here, or in the U. Tokyo Learning Management System (UT ITC-LMS).
                (4) The real time blackboard-writing style on Zoom will be adopted,
                      but the lecture notes will still be made available online prior to the lecture both in this page and UT ITC-LMS.
                      This plan assumes that we can secure 1hr45min every week, though.
                (6) Homework submission deadline: Feb. 1 (Mon), 23:55.
                (7) Week 13: Jan 7 (Thu)

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

Sep. 28: note-01 hw-01 path integral formulation of quantum mechanics
                                          [[FH 3, 8], [Na 2.1], [AS 3.2], [XGW p.24], 9.1]
Oct. 05: note-02 hw-02 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]]
Oct. 12: note-03 hw-03 introduction // S-matrix, decay rate, cross section, spectral representation
                                          [4.5, 7.1, [W-I 3.1, 3.2, 10.7]]
Oct. 19: note-04 hw-04 LSZ formula, Feynman rule, other correlators //
                                          [7.2, 4.2--4.4, 4.6--4.8, [W-I 4.3], 3.2, 3.3, 3.5, [W-I 6., 8.]]
                                          [For section 3.4 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. 26: note-05 hw-05 vector field propagator, e+e- to mu+mu- unpolarized (high energy, threshold)
                                          [5.1]
Nov. 02: note-06 ------ e+e- to mu+mu- (polarized), crossing symmetry, t-channel 2to2, non-relativistic limit, Mott scattering
                                          [5.1--5.4]
Nov. 09: note-07 hw-07 L-S coupling, Compton/Thomson scattering //
                                          [5.4, 5.5, [Ni 3.4, 3.5]]
Nov. 16: note-08 ------ 1-loop computation (anomalous magnetic moment)
                                          [6.2, 6.3]
Nov. 30: note-09 ------ 1-loop computation (cont'd) // Bethe Salpeter equation
                                          [6.2, 6.3, [LL4 125], [T 10]]
Dec. 07: [use -09] hw-10 Bethe Salpeter equation (cont'd), fine/hyperfine structure, Lamb shift
                                          [[LL4 125], [T 10], [LL4 33, 34], [Ni 1.10], [LL4 123], 7.5, Wikipedia]
Dec. 14: note-11 hw-11 atomic transition // partial wave unitarity
                                          [??, [W-I 3.6--3.8]]
Dec. 21: note-12 hw-12 optical theorem // low-energy effective theory //
                                          [7.3]
Jan. 07: note-13 ----- path integral for QFT, free energy, effective potential
                                          [11.3-5, 16.6, [W-II 16.1-3, 21.6]]
Jan. 18: note-14 hw-14 background field method, thermal field theory (imaginary time formalism)
                                          [8, 9.2, 9.5, [LB 2.1, 2.6, 3.1]]
Jan. 25: note-15 hw-15 coarse graining, real time (Keldysh) formalism
                                          [[LB, K (see Ref. for Week 4)], [hw E-2]]

Advanced homework problems: D-1, ..., D-5 and E-1, ..., E-6.

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

For the following homework problems, a sample solution has been prepared in a pdf file. Will be made available through ITC-LMS after submission.
I-1 (harm.oscil), II-2 (chem.pot) II-3 (geom.quant), III-2 (conduction, Friedel), V-1 (Dirac br), VII-1 (LS coupl), VII-3 (2to3), E-4 (CS) as of Sept. 28.
V-2 (spin in s-channel), V-3 (FB asymmetry) added Oct. 26.
XI-1 (E2, M1 emission), XI-3 (partial wave), XII-1 (neutrino) added Dec. 28
XIV-1 (Matsubara.p), A-XIV-f (harm.oscil) added Jan. 14 + XV-2 (flct.disp.thm)

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),
[XGW] X.G. Wen, Quantum Field Theory of Many-body Systems

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: All the reports on the homework problems (exception see below) are supposed to be submitted through the U Tokyo ITC-LMS. We request that the file names contain the problem number that you worked on in that report (e.g., II-1***.pdf or ***-IV-2-IX-1.txt).
E-mail submission: One pagagraph summary each week (counted as a category [A] problem) can be submitted by sending an e-mail to the address announced in the classroom. (no attachment file please in this option)
                I ask that the Subject line is written as "Date of a relevant lecture" "student ID" [example: Sep 26 ss921456]