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)

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

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.

Extra exercises:

• Extra sheet, 1 posted October 27, pdf below.

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