String/M theory, Master course, 5p, Lp IV 2007
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2007: Tuesday 20 March at 15.15 in Origo 6115
(the physics building called Origo, 6th floor, north wing).
Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C
Literature: "A first course in string theory", Barton Zwiebach,
(Cambridge university press 2004).
Available on the net for <600 SEK, and at Cremona.
Tentative study plan for the course:
week 1 (calender week 12): chaps 1-3
week 2 (calender week 13): chaps 4-6
Easter holiday (calender weeks 14 and 15)
week 3 (calender week 16): chaps 7-10
week 4 (calender week 17): chaps 11-13
week 5(1/2 calender week 18): chap 21 and lecture notes on superstrings
week 6 (calender week 19): parts of chaps 14-16
week 7(1/2 calender week 20): parts of chaps 17-20
week 8 (calender week 21): parts of chaps 17-20
week 9 (calender week 22): examination
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NEW Schedule: All lectures in Origo 6115
Mondays at 10.00-12.00
Tuesdays at 13.15-15.00
Fridays at 08.00-10.00
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Additional reading:
Non-technical string literature:
An excellent popular account of the fundamental questions and
ideas of modern string/M theory can be found in
"The elegent universe", by Brian Greene (Jonathan Cape 1999).
Additional string literature: (abbreviation in bracket)
1. M. Green, J. Schwarz and E. Witten (GSW), "Superstring theory",
volume I and II
(Cambridge University Press 1987).
2. J. Polchinski (JP), "String theory", volume I and II
(Cambridge University Press 1998).
3. D. Lüst and S. Theisen (LT), "Lectures on string theory",
(346 Lecture Notes in Physics, Springer Verlag 1989).
You can find the book here as Part 2, Part 3.
"Part one",
4. C. V. Johnson, "D-branes" (Cambridge monographs on mathematical physics 2003)
5. K. Becker, M. Becker, and J.H. Schwarz (BBS), "String theory and M-theory",
(Cambridge Univ Press 2007)
Recent books debating the pros and cons of string theory
L. Smolin, "The trouble with physics" (Houghton Mifflin Company, 2006)
P. Woit, "Not even wrong" (Jonathan Cape, 2006)
see also comments on these by J. Polchinski:
Guest Blogger: Joe Polchinski on String Debates
General high-energy physics:
A very nice overview of elementary particle physics, gravitation and cosmology, Kaluza-Klein,
supersymmetry and introductory string theory can be found in
"Particle physics and cosmology", by P.D.B. Collins, A.D. Martin and E.J. Squires (Wiley 1989).
Literature discussing unification and reductionism
"Dreams of a final theory", Stephen Weinberg (Vintage 1992): Very good!!
"The emperor's new mind", Roger Penrose (Penguin 1989)
Some articles from Physics Today:
Witten, Physics Today, April 1996, p. 24-30
Kane, Physics Today, Febr 1997, p. 40-42
Collins, Physics Today, March 1997, p. 19-22
Witten, Physics Today, May 1997, p. 28-33
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About the book
The 2006 version of the Master course String/M theory is based on the
new book "A first course in string theory" by Barton Zwiebach. This book
gives an extremely pedagogical introduction to this rather difficult subject
by starting from physics familiar to all undergraduate students having
studied physics for two years at the university. The required knowledge of
mathematics is kept at a minimum by providing detail explanations of all
the mathematics used that is not part of the first year mathematics
curriculum.
All the necessary aspects of field theory, from electromagnetism to gravity,
and quantum mechanics are explained from scratch and developed just to the
level needed for the application in question.
A large number of exercises and problems appear at the end of each chapter
some of which will be used as home exam problems for this course.
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Examination:
Home problems and a successful oral exam for highest mark (CTH: 5, GU: VG)
Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points
4 requires 60% of the total points
5 requires 80% of the total points plus a successful oral exam
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NOTE: The links below suggest extra reading material that is not included in the course requirments
and will not appear in the oral exam (unless the article is used in a home exam problem).
NOTE: The exercises in the text called "Quick calculations" are
generally very nice and give a good check that you have understood the material.
You should try to do them without exception.
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1st WEEK (calender week 12): Introduction and basic aspects from field theory
Lecture 1: Tuesday March 20, at 15.15 Introduction: Chap 1 in Zwiebach´s book (BZ)
Further reading:
String/M theory introduces extra dimensions. Have a look at the history of such
by reading Stanley Deser's account
"The many dimensions of dimension",
and the first few pages in the article
"Perspectives on issues beyond the standard model"
by G. Kane.
Lecture 2: Wednesday March 21 at 08.00 Units, special relativity and extra dimensions
(Chapter 2 in BZ)
Further reading:
For a recent discussion of units and fundamental constants in nature, see Mike Duff
"Comment on time variation of fundamental constants ".
and for comments on extra dimensions, read the first three or four pages in F. Ferugio's
review article
"Extra dimension in particle physics".
Lecture 3: Friday March 23 at 08.00 Field theories in various dimensions, the Planck length
(Chapter 3 in BZ)
Recommended exercises from BZ: 2.2, 2.3, 3.3, 3.4 and 3.7
Home exam problem 1: Solve problem 2.1 in BZ.. Read the article by M. Duff (see link
from lecture 2)
and explain the difference between fundamental dimensionful constants like c, and coupling
constants like e .
NOTE: Only problem 2.1 needs to be handed in , but questions on the article by Duff may
occur in the oral exam.
Home exam problem 2: Solve problem 2.4 in BZ.
Home exam problem 3: Solve problem 3.9 in BZ.
Dead-line for handing in home exam problems 1-3 is March 30.
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2nd WEEK (calender week 13): Point particles and strings: the classical story
Lecture 4: Monday March 26 at 10.00 Non-relativistic strings and Lagrangian formulations (Chapter 4 in BZ)
Lecture 5: Tuesday March 27 at 13.15 The relativistic point particle (Chapter 5 in BZ)
Lecture 6: Friday March 30 at 08.00 The relativistic string (Chapter 6 in BZ)
Recommended exercises: BZ problems 4.6, 5.1, 5.2, 5.4, 5.5, and 5.7 if you have taken GR.
Home exam problem 4: Solve problem 4.3 in BZ
Home exam problem 5: Solve problem 5.6 in BZ
Home exam problem 6: Solve problem 6.6 in BZ
Dead-line for handing in home exam problems 4, 5 and 6 is April 20.
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3rd WEEK (calender week 16): More classical string theory
Lecture 7: Monday April 16 at 10.00 Classical string motion (Chapter 7 in BZ).
Lecture 8: Tuesday April 17 at 13.15
World-sheet currents and the slope parameter \alpha^{\prime} (Chapter 8 in BZ)
Lecture 9: Friday April 20 at 08.00 The light-cone relativistic string and field theory (Chapters 9 and 10 in BZ)
Recommended exercises: BZ problems 7.2, 8.2, 8.4, 9.1, 9.3, 10.2 and 10.3,
Home exam problem 7: Solve problem 7.5 in BZ
Home exam problem 8: Solve problem 8.3 in BZ
Home exam problem 9: Solve problem 9.2 in BZ
Home exam problem 10: Solve problem 10.6 in BZ
Dead-line for handing in home exam problems 7 to 10 is May 4
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4th WEEK (calender week 17):
Light cone particles, strings and superstrings: the quantum case.
Lecture 10: Monday April 23 at 10.00
The relativistic quantum point particle (Chapter 11 in BZ)
Read this chapter carefully; many important points are here explained in a
simpler setting than string theory: gauge fixing, compensating transformations,
quantization both in the light cone gauge and covariant (as done later in Chapter 21 for the string).
Lecture 11: Tuesday April 24 at 13.15
The relativistic quantum open string (Chapter 12 in BZ)
This chapter contains for the first time in this course material that we normally
refer to as "string theory": quantized string coordinates and Virasoro generators and their
algebra, and the mass spectrum and its interpretation. These last concepts are
vital for understanding the rest of the course.
Lecture 12: Friday April 27 at 08.00
The relativistic closed string (Chapter 13 in BZ)
Read the bosonic closed string material carefully and have a look at the last section
on the superstring. We will start week 5 by summarizing the material in chaps 11-13 and
then spend the rest of that week discussing covariant string theory (chap 21) and superstring
theory (lecture notes).
When we turn to applications in the second part of the book ("Developments") it is of vital
importance to fully master the arguments and results of the chapters 11-13 in BZ.
"The string landscape": Recent developments in string/M theory point towards a more
complex connection between the theory and our dynamical universe. This has led to a heated
debate about the role of the anthropic principle in the context of the "landscape".
For an introductory discussion of the "string landscape", see Stephen Weinberg's paper
"Living in the multiverse".
In particular the final paragraph gives a feeling for the "heat" in this debate.
Recommended exercises: BZ problem 11.4, 11.5, 12.2 and 12.7
Home exam problem 11: Solve problem 11.6 in BZ
Home exam problem 12: Solve problem 12.3 in BZ
Home exam problem 13: Solve problem 12.10 in BZ
Home exam problem 14: Solve problem 13.5 in BZ
Dead-line for handing in home exam problems 10 to 14 is May 11
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5th WEEK (calender week 18): Covariant aspects of quantized strings and superstrings
NOTE: Lectures this week on Thursday at 13.15 and on Friday at 08.00.
Lecture 13: Thursday May 3
Review of the light cone quantization of open and closed bosonic strings (chaps 12 and 13).
Covariant quantization of the bosonic string (Chapter 21)
Lecture 14: Friday May 4 Cont. with chap 21. Intro to quantized superstrings
(Read lecture notes and section 13.5 in BZ)
Recommended exercises: BZ problem 21.3 and 21.5
Home exam problem 15: Solve problem 21.2 in BZ
Home exam problem 16: Solve problem 13.7 in BZ
Dead-line for handing in home exam problems 15 and 16 is May 21
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6th WEEK (calender week 19): Advanced topics: D-branes
NOTE: only one lecture this week Friday 08.00-12.00
Lecture 15: at 08.00 Friday May 11
D-branes: parts of Chapter 14 in BZ
Lecture 18: at 10.00 Friday May 11
String charge: Parts of Chap 15 in BZ
Recommended exercises: 14.1 and 15.3
Home exam problem 17: Solve problem 14.6 in BZ
Home exam problem 18: Solve problem 15.7 in BZ
Dead-line for handing in home exam problems 17 and 18 is May 21
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7th WEEK (calender week 20): Advanced topics: Dualities
Lecture 19: at 10.00 Monday May 14
T-duality in string theory: Parts of Chaps 17 and 18 in BZ
Lecture 20: at 13.15 Tuesday May 15
Maxwell and Born-Infeld electrodynamics on D-branes: Chaps 19 and 20
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8th week (calender weeks 21): Branes, supergravity, duality and M-theory
Lecture 21: at 10.00 Monday May 21
Effective field theories on branes and in the bulk, supergravity; overview
(lecture notes only)
Lecture 22: at 13.15 Tuesday May 22
Introduction to M-theory (lecture notes only)
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9th week(calender weeks 22): Examination week
Examination:Please schecule the oral exam with me a soon as possible.
The last day possible for the oral exam is Wednesday May 30.
NOTE: Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points
4 requires 60% of the total points
5 requires 80% of the total points plus a successful oral exam
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