String/M theory, Master course, 5p, Lp IV 2005
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2005: April 4 at 10.00 in Origo 6115
(the physics building called Origo, 6th floor, north wing).
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Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C
Schedule: Monday, Wednesday, and Friday at 10.00 in Origo 6115.
Literature: "A first course in string theory", Barton Zwiebach,
(Cambridge university press 2004) Available on the net for <600 SEK.
Examination:
Home problems and a successful oral exam for highest mark (CTH: 5, GU: VG)
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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)
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 ereperor'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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The 2005 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
point where it is 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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WEEKLY SCHEDULE Lp IV 2005
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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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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).
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1st WEEK (calender week 14): Introduction and basic aspects from field theory
Lecture 1: Introduction (Chapter 1 in B. Zwiebach's (BZ) book)
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: 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: 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 April 20.
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2nd WEEK (calender week 15): Point particles and strings: the classical story
Lecture 4: Non-relativistic strings and Lagrangian formulations (Chapter 4 in BZ)
Lecture 5: The relativistic point particle (Chapter 5 in BZ)
Lecture 6: 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 27.
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3rd WEEK (calender week 16): More classical string theory
Lecture 7: Classical string motion (Chapter 7 in BZ).
Advanced track 1 on an alternative action, the "Polyakov action".
Lecture 8: World-sheet currents and the slope parameter \alpha^{\prime} (Chapter 8 in BZ)
Lecture 9: The light-cone relativistic string (Chapter 9 in BZ)
Recommended exercises: BZ problems 7.2, 8.2, 8.4, 9.1, and 9.3
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
Dead-line for handing in home exam problems 7 to 9 is May 4
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4th WEEK (calender week 17): Light cone strings and field theories: XSclassical and quantum
Lecture 10: Light cone fields and particles (Chapter 10 in BZ)
Lecture 11: 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 covariant and in the light cone gauge (as done later for the string).
Lecture 12: The relativistic quantum open string (Chapter 12 in BZ)
This chapter contains for the first time in this course material that what 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.
Recommended exercises: BZ problem 10.2, 10.3, 11.4, 11.5, 12.2 and 12.7
Home exam problem 10: Solve problem 10.6 in BZ
Home exam problem 11: Solve problem 11.6 in BZ
Home exam problem 12: Solve problem 12.3 in BZ
Dead-line for handing in home exam problems 10 to 12 is May 11
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5th WEEK (calender week 18): The quantum string
Lecture 13: The relativistic quantum open string; continued (Chapter 12 in BZ)
Lecture 14: The relativistic quantum closed string (Chapter 13 in BZ)
Recommended exercises: BZ problem 12.4, 12.5, 12.11, 13.2 and 13.7
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 13 and 14 is May 18
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6th WEEK (calender week 19): Advanced aspects of string theory
Lecture 15: Covariant quantization of the bosonic string (Chapter 21 in BZ)
Lecture 16: Quantized superstrings
(Read lecture notes and section 13.5 in BZ)
Lecture 17: More on the superstrings, some effective field theory, and the
role of M-theory (lecture notes only)
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 24
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7th WEEK (calender week 20): Advanced topics; D-branes
Lecture 18: Starts at 09.00 More on superstrings, the full list of superstrings
Lecture 19: Starts at 09.00 Dp-branes (parts of Chapter 14 and 15 in BZ)
Lecture 20: T-duality and Overview (parts of Chapter 17 - 20 in BZ)
Recommended exercises: 14.1 and 15.3
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8th WEEK (calender week 21): Examination week
Please schecule the oral exam with me a soon as possible.
The last day possible for the oral exam is May 31.
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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