Stijn J. van Tongeren

Summer Semester of 2022: General Relativity.

Lectures (IRIS 1.207): Wednesdays 15:15-16:45, Fridays 15:15-16:45 (biweekly)
Tutorials (IRIS 1.207): Fridays 15:15-16:45 (biweekly, possibly to be shifted due to Dies academicus)
We will have a 5 minute break in the middle of our time-slots, and run over at the end by 5 minutes.
NO LECTURE OR TUTORIAL on Wednesday 27 April (Dies academicus from noon).

Course organization:

We will mainly follow the book "Spacetime and Geometry" by Sean M. Carroll. As an alternative, if necessary you can make do with the "Lecture Notes on General Relativity" by the same author, which covers roughly the same material.
There will be a written examination at the end of the course on 27 July 2022, 15:00-17:00.

Moodle page: https://moodle.hu-berlin.de/course/view.php?id=113516 (enrollment key: GR)

Winter Semester of 2020: Group theory in physics.

Lectures: Tuesdays 11:15-12:45, Thursdays biweekly 11:15-12:45
Tutorials: Thursdays biweekly 11:15-12:45

Course organization:

Due to the ongoing pandemic, lectures and tutorials will take place online.
We will mainly follow sections of the book ''Lie Groups, Lie Algebras, and Representations'' by Brian C. Hall, second edition.
There will be a written examination at the end of the course.
Further details on the course Moodle page.

Summer Semester of 2019: Group theory in physics.

Lectures: Tuesdays 11:15-12:45, Thursdays biweekly 11:15-12:45, room 207 IRIS building ZGW6
Tutorials: Thursdays biweekly 11:15-12:45, room 207 IRIS building ZGW6

Course organization:

The first part of the course, on discrete groups, will follow a set of lecture notes to be distributed in class. The second, main part of the class, on Lie groups, will follow sections of the book ''Lie Groups, Lie Algebras, and Representations'' by Brian C. Hall, second edition. Sections discussed are listed below, with corresponding sections for the first edition of the book by Hall in [square brackets].
Exercise sheets should be completed by the start of the tutorial class, where students will present their solutions.
There will be a written examination at the end of the course, on Tuesday the 23rd of July, 11:00-13:00 (it starts at 11 sharp!). Question hours: 12 July 11:00-12:00, 22 July 14:00-15:00.

Material covered:

Lecture 1 - all of section 1, and section 2.1 of lecture notes
Lecture 2 - sections 2.2, 2.3 and half of 2.4
Lecture 3 - up to section 3.2
Lecture 4 - sections 3.2 and 3.3
Lecture 5 - sections 3.4 and 3.5
Lecture 6 - remainder of notes (roughly)
Lecture 7 - sections 1.1 and 1.2 of book by Hall [1.1, 1.2 of first edition]
Lecture 8 - 1.3 up to proof of proposition 1.17 [1.3, 1.4, 1.5 except fundamental groups/SO(3) discussion]
Lecture 9 - remainder of 1.3, 1.4 [1.6, except this misses the discussion that Phi is onto SO(3)] (please read 1.5 [1.8] yourself)
Lecture 10 - 2.1, 2.2, 2.3 [2.1, 2.2, 2.3]
Lecture 11 - 2.4, 2.5 [2.4, 1.7 except this misses P = exp X]
Lecture 12 - 3.1-3.3, most of 3.4 [parts of 2.8 (misses notion of simple Lie algebra), parts of 2.5 and 2.6]
Lecture 13 - remainder of 3.4, 3.5, 3.6 [remainders of 2.5, 2.6, and 2.8]
Lecture 14 - 3.7, most of 3.8 [first half of 2.7]
Lecture 15 - Remainder of 3.8, 4.1, most of 4.2 [remainder of 2.7, 4.1, 4.2, 4.3.1-3, most of 4.3.4]
Lecture 16 - Remainder of 4.2, 4.3, first half of 4.4 [remainder of 4.3.4, 4.5, 4.6, 4.7, part of 4.8]
Lecture 17 - 4.4, 4.5, 4.6 [4.8, 4.10 (integration on group is discussed slightly differently, but same conclusion)]
Lecture 18 - 4.7, 5.1, 5.4, 5.3 [4.4, missing the discussion of reps of SO(3) vs reps of SU(2), 3.2, 3.3]
Lecture 19 (short) - 5.3, 5.5, 5.6 [3.3, 3.4]
Lecture 20 - 5.7, 5.8 [3,6, 3.7]
Lecture 21 - 5.9, 5.10 [3.8, slightly different discussion but basically the same material covered]

We did not get to the final topic of the Lorentz group and algebra (relation to SL(2,C), topology, finite dimensional representations). Most of what I would have liked to discuss can be found in "The Quantum Theory of Fields" by Steven Weinberg, volume 1, section 2.3, and pages 86-89, 214, 216-217, 229-232, though of course this does not emphasize connections to the earlier lectures.

Exercise sheets (see below for pdf):

Sheet 1 posted 11 April 2019, to be discussed 18 April 2019
Sheet 2 posted 25 April 2019, to be discussed 2 May 2019
Sheet 3 posted 9 May 2019, to be discussed 16 May 2019
Sheet 4 posted 17 May 2019, to be discussed 4 June 2019 (note the shift due to Ascension day!)
Sheet 5 posted 6 June 2019, to be discussed 20 June 2019
Sheet 6 posted 18 June 2019, to be discussed 27 June 2019
Sheet 7 posted 20 June 2019, to be finished by 4 July 2019

Group_Theory_Sheet_1 (1).pdf

Group_Theory_Sheet_2 (1).pdf

Group_Theory_Sheet_3 (1).pdf

Group_Theory_Sheet_4 (1).pdf

Group_Theory_Sheet_5 (1).pdf

Group_Theory_Sheet_6_shortened.pdf

Group_Theory_Sheet_7 (1).pdf

Summer semester of 2018: Introduction to string theory.

Lectures: Tuesdays biweekly 13:15-14:45, Wednesdays 11:15-13:45, room 207 IRIS building ZGW6
Tutorials: Tuesdays biweekly 13:15-14:45, room 207 IRIS building ZGW6

Course organization:

We will mainly follow David Tong's lecture notes that are freely available online.
Tutorials will mainly take the form of problem solving sessions. Problem sheets will be posted in advance; students are advised to look at them before class. Active participation in the tutorials is strongly encouraged. Each student will be required to write up a detailed solution to one of the tutorial problems (in LaTeX), to form a set of solution sheets for all students by the end of the course.
Examination: there will be a written exam on the 25th of July (one week after the last lecture), plan accordingly. A retake exam will be possible only in special circumstances.

Material covered:

Lecture 1: Most of section 0 of Tong's notes.
Lecture 2: Section 1.1
Lecture 3: Sections 1.2-1.3.1
Lecture 4: Up to (not including) section 2.1.1
Lecture 5: Up to and including page 37
Lecture 6: Up to and including page 44
Lecture 7: Remainder of section 2
Lecture 8: Sections 4-4.1.2
Lecture 9: Up to halfway down page 75.
Lecture 10: Up to top of page 82.
Lecture 11: Up to 4.4.3.
Lecture 12: Up to and including page 95.
Lecture 13: up to and including page 101
Lecture 14: Rest of chapter 4 excluding section 4.7, start of chapter 5
Lecture 15: Up to middle of page 115.
Lecture 16: Remainder of chapter 5, except sections 5.3.2 and 5.4.2.
Lecture 17: - intermission - group theory review lecture
Lecture 18: Sections 6.1-6.2.1.
Lecture 19: Remainder of section 6.2, section 6.4.1 (please read remainder of 6.4 yourself)
Lecture 20: Sections 7-7.2.1
Lecture 21: Sections 7.2.2-7.4.1

Exercise sheets:

String_Theory_Sheet_1.pdf

String_Theory_Sheet_2.pdf

String_Theory_Sheet_3.pdf

String_Theory_Sheet_4.pdf

String_Theory_Sheet_5.pdf

String_Theory_Sheet_6.pdf

Winter semester of 2017: Group theory in physics.

Lectures: Tuesdays 13:15-14:45, Wednesdays biweekly 11:15-12:45, room 207 IRIS building ZGW6
Tutorials: Wednesdays biweekly 11:15-12:45, room 207 IRIS building ZGW6

Course organization:

The first part of the course, on discrete groups, will follow a set of lecture notes to be distributed in class. The second part of the class, on Lie groups, will follow sections of the book ''Lie Groups, Lie Algebras, and Representations'' by Brian C. Hall, second edition. Sections discussed are listed below, with corresponding sections for the first edition of the book by Hall in [square brackets].
Exercise sheets are to be completed by the start of the tutorial class, where students will present their solutions.
There will be a written examination on Tuesday March 6, 13:00-15:00, room 207 IRIS building ZGW6. Question hours: Tuesday February 27, from 13:00-15:00. Retake exam: Tuesday April 3, 11:00-13:00.

Material covered:

Lecture 1 - sections 1 and 2.0 of notes.
Lecture 2 - sections 2.1 and 2.2, 2.3 up to and including proof of Proposition 2.6.
Lecture 3 - remainder of section 2.
Lecture 4 - section 3 up to and including example 3.3
Lecture 5 - up to section 3.5
Lecture 6 - sections 3.5 and 3.7 (please read section 3.6 at home)
Lecture 7 - section 4 of notes (roughly) + 1.1, 1.2.1 [1.1, 1.2.1, 1.2.2] of book (Hall)
Lecture 8 - 1.2.2/3/4/5/6 [1.2.3/4/5/6/7/8] of book (please read 1.2.8 [n.a.] if interested)
Lecture 9 - 1.3.1, 1.3.2, 1.3.3, first half of 1.3.4 [1.3, 1.4, 1.5 except fundamental groups/SO(3) discussion] of book
Lecture 10 - remainder of 1.3.4, 1.4 [1.6, except this misses the discussion that Phi is onto SO(3)] (please read 1.5 [1.8] yourself)
Lecture 11 - 2.1, 2.2, 2.3 [2.1, 2.2, 2.3]
Lecture 12 - 2.4, 2.5 [2.4, 1.7 except this misses P = exp X]
Lecture 13 - 3.1, 3.2, 3.3, first half of 3.4 [parts of 2.8 (misses notion of simple Lie algebra), parts of 2.5 and 2.6]
Lecture 14 - remainder of 3.4, 3.5, 3.6 [remainders of 2.5, 2.6, and 2.8]
Lecture 15 - 3.7, beginning of 3.8 [first half of 2.7]
Lecture 16 - Remainder of 3.8, 4.1 [remainder of 2.7, 4.1, 4.2]
Lecture 17 - 4.2, 4.3 [4.3.1-4, 4.5, 4.6, 4.7]
Lecture 18 - 4.4, 4.5 [4.8, 4.10 (integration on group is discussed slightly differently, but same conclusion)]
Lecture 19 - 4.6, 4.7 [4.4, missing the discussion of reps of SO(3) vs reps of SU(2)]
Lecture 20 - 5.1, 5.3 5.4, 5.5, 5.6 [3.2, 3.3, 3.4]
Lecture 21 - 5.7 [3.6]
Lecture 22 - 5.8, 5.9, 5.10 [3.7, 3.8, slightly different discussion but basically the same material covered]
Lecture 23 - The Lorentz group and algebra (relation to SL(2,C), topology, finite dimensional representations). Most of what I discussed can be found in "The Quantum Theory of Fields" by Steven Weinberg, volume 1, section 2.3, and pages 86-89, 214, 216-217, 229-232, though this does not emphasize connections to the earlier lectures.

Exercise sheets:

First tutorial, 25 October, sheet 1, pdf below.
Second tutorial, 15 November, sheet 2, pdf below.
Third tutorial, 29 November, sheet 3, pdf below.
Fourth tutorial, 13 December, sheet 4, pdf below.
Fifth tutorial, 10 January, sheet 5, pdf below.
Sixth tutorial, 24 January, sheet 6, pdf below.
Seventh tutorial, 7 February, sheet 7, pdf below.

Group_Theory_Sheet_1.pdf

Group_Theory_Sheet_2.pdf

Group_Theory_Sheet_3.pdf

Group_Theory_Sheet_4.pdf

Group_Theory_Sheet_5.pdf

Group_Theory_Sheet_6.pdf

Group_Theory_Sheet_7.pdf

Extra exercises:

Extra sheet, 1 posted October 27, pdf below.

Group_Theory_practice_Sheet_1.pdf

Summer semester of 2017: Introduction to string theory.

Lectures: Tuesdays 11:15-12:45, Thursdays biweekly 13:15-14:45, room 221 IRIS building ZGW6
Tutorials: Thursdays biweekly 13:15-14:45, room 221 IRIS building ZGW6

Course organization:

We will mainly follow David Tong's lecture notes that are freely available online. These notes cover more than our course will. Relevant sections will be listed.
Tutorials will mainly be problem solving sessions. Problem sheets will be posted in advance -- students are advised to look at them before class. Active participation in the tutorials is strongly encouraged. Each student will be required to write up a detailed solution to one of the tutorial problems (in LaTeX), to form a set of solution sheets for all students by the end of the course.
Examination details will depend on the number of students.

Tutorials and exercise sheets

First tutorial 27 April, exercise sheet 1. Please try to complete exercises 1 and 2 before class, and have look at the rest.
Second tutorial 11 May, exercise sheet 2.
Third tutorial 24 May 11-13:00 (special date!!), exercise sheet 3.
Fourth tutorial 8 June, exercise sheet 4.
Fifth tutorial 22 June, exercise sheet 5.
Sixth tutorial 13 July, exercise sheet 6.

Please try to have a look at the problems before class. Pdfs below.

Sheet_1.pdf

Sheet_2.pdf

Sheet_3.pdf

Sheet_4.pdf

Sheet_5.pdf

Sheet_6.pdf

Winter semester 2016: tutorials for Introduction to quantum field theory.

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