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Abstract/Syllabus:
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Zwiebach, Barton, and Alan Guth, 8.251 String Theory for Undergraduates, Spring 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA
String Theory for Undergraduates
Spring 2007
A torus is built from a cylinder of circumference 2π and length T by gluing the edges with a twist angle θ. The set of inequivalent tori is represented by the points in the orange region. In all these tori the shortest geodesic has length greater than or equal to 2π. (Image by MIT OCW.)
Course Description
This course introduces string theory to undergraduate and is based upon Prof. Zwiebach's textbook entitled A First Course in String Theory. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics.
Syllabus
Prerequisites
8.033 (Relativity), 8.044 (Statistical Physics I), and 8.05 (Quantum Physics II).
Textbook
Zwiebach, Barton. A First Course in String Theory. New York, NY: Cambridge University Press, 2004. ISBN: 9780521831437.
Additional Reference
A new readable book at the graduate level is:
Becker, Katrin, Melanie Becker, and John H. Schwarz. String Theory and M-Theory: A Modern Introduction. Cambridge, UK: Cambridge University Press, 2007. ISBN: 9780521860697.
Homework
There will be weekly homework. No late homework will be accepted. Students will be able to drop one homework - the one with the lowest grade - from their record.
Tests
There will be two tests and a final exam.
Grading
Grading criteria.
| ACTIVITIES |
PERCENTAGES |
| Homework |
35% |
| Test 1 |
20% |
| Test 2 |
20% |
| Final exam |
25% |
Calendar
Course calendar.
| SES # |
TOPICS |
KEY DATES |
| 1 |
Announcements, introduction
Lorentz transformations
Light-cone coordinates
|
|
| 2 |
Energy and momentum
Compact dimensions, orbifolds
Quantum mechanics and the square well
|
|
| 3 |
Relativistic electrodynamics
Gauss' law
Gravitation and Planck's length
|
Homework 1 due |
| 4 |
Gravitational potentials, compactification, and large extra dimensions |
|
| 5 |
Nonrelativistic strings and lagrangian mechanics |
Homework 2 due |
| 6 |
The relativistic point particle: Action, reparametrizations, and equations of motion |
|
| 7 |
Area formula for spatial surfaces |
Homework 3 due |
| 8 |
Area formula for spatial surfaces (cont.) |
|
| 9 |
Change of variables |
Homework 4 due |
| 10 |
Relativistic strings: Nambu-Goto action, equations of motion and boundary conditions |
Homework 5 due |
| 11 |
Static gauge, transverse velocity, and string action
Motion of free open string endpoints
|
|
| 12 |
The sigma-parametrization
Equations of motion and virasoro constraints
General motion for open strings
Rotating open strings
|
Homework 6 due |
| |
Test 1 |
|
| 13 |
Periodicity conditions for the motion of closed strings
The formation of cusps
Conserved currents in E&M
Conserved charges in lagrangian mechanics
|
|
| 14 |
Momentum charges for the string
Lorentz charges for the strings
Angular momentum of the rotating string
Discuss alpha' and the string length l_s
General gauges: fixing tau and natural units
|
Homework 7 due |
| 15 |
Solution of the open string motion in the light-cone gauge |
|
| 16 |
Light-cone fields and particles |
|
| 17 |
Light-cone fields and particles (cont.) |
Homework 8 due |
| 18 |
Open strings |
Homework 9 due |
| 19 |
Critical dimension
Constructing the state space
Tachyons
|
|
| 20 |
Closed strings |
Homework 10 due |
| 21 |
Wrap-up of closed strings
Superstrings
|
|
| |
Test 2 |
|
| 22 |
Superstrings (cont.) |
|
| 23 |
Closed strings
Heterotic string theory
|
|
| 24 |
Dp-branes
Parallel Dp's
|
Homework 11 due |
| 25 |
Dp-branes (cont.) |
|
| 26 |
Final exam review |
|
| |
Final exam week |
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Further Reading:
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Readings
Textbook
The required text for this class is:
Zwiebach, Barton. A First Course in String Theory. New York, NY: Cambridge University Press, 2004. ISBN: 9780521831437.
All readings are assigned out of this book.
Additional Reference
A new readable book at the graduate level is:
Becker, Katrin, Melanie Becker, and John H. Schwarz. String Theory and M-Theory: A Modern Introduction. Cambridge, UK: Cambridge University Press, 2007. ISBN: 9780521860697.
Course readings.
| SES # |
TOPICS |
READINGS |
| 1 |
Announcements, introduction
Lorentz transformations
Light-cone coordinates
|
Sections 2.1-2.3 |
| 2 |
Energy and momentum
Compact dimensions, orbifolds
Quantum mechanics and the square well
|
Sections 2.4-2.9 |
| 3 |
Relativistic electrodynamics
Gauss' law
Gravitation and Planck's length
|
Sections 3.1-3.6 |
| 4 |
Gravitational potentials, compactification, and large extra dimensions |
Sections 3.7-3.10 |
| 5 |
Nonrelativistic strings and Lagrangian mechanics |
Chapter 4 |
| 6 |
The relativistic point particle: Action, reparametrizations, and equations of motion |
Chapter 5 |
| 7 |
Area formula for spatial surfaces |
|
| 8 |
Area formula for spatial surfaces (cont.) |
|
| 9 |
Change of variables |
|
| 10 |
Relativistic strings: Nambu-Goto action, equations of motion and boundary conditions |
Sections 6.1-6.5 |
| 11 |
Static gauge, transverse velocity, and string action
Motion of free open string endpoints
|
Sections 6.6-6.9 |
| 12 |
The sigma-parametrization
Equations of motion and virasoro constraints
General motion for open strings
Rotating open strings
|
Chapter 7 |
| |
Test 1 |
|
| 13 |
Periodicity conditions for the motion of closed strings
The formation of cusps
Conserved currents in E&M
Conserved charges in lagrangian mechanics
|
|
| 14 |
Momentum charges for the string
Lorentz charges for the strings
Angular momentum of the rotating string
Discuss alpha' and the string length l_s
General gauges: fixing tau and natural units
|
Sections 8.4-8.6, 9.1 |
| 15 |
Solution of the open string motion in the light-cone gauge |
Sections 9.2-9.4 |
| 16 |
Light-cone fields and particles |
Sections 9.5-10.1 |
| 17 |
Light-cone fields and particles (cont.) |
Sections 10.2-10.4 |
| 18 |
Open strings |
|
| 19 |
Critical dimension
Constructing the state space
Tachyons
|
|
| 20 |
Closed strings |
|
| 21 |
Wrap-up of closed strings
Superstrings
|
|
| |
Test 2 |
|
| 22 |
Superstrings (cont.) |
|
| 23 |
Closed strings
Heterotic string theory
|
|
| 24 |
Dp-branes
Parallel Dp's
|
|
| 25 |
Dp-branes (cont.) |
|
| 26 |
Final exam review |
|
| |
Final exam week |
|
| 12 |
The sigma-parametrization
Equations of motion and virasoro constraints
General motion for open strings
Rotating open strings
|
Chapter 7 |
| |
Test 1 |
|
| 13 |
Periodicity conditions for the motion of closed strings
The formation of cusps
Conserved currents in E&M
Conserved charges in lagrangian mechanics
|
|
| 14 |
Momentum charges for the string
Lorentz charges for the strings
Angular momentum of the rotating string
Discuss alpha' and the string length l_s
General gauges: fixing tau and natural units
|
Sections 8.4-8.6, 9.1 |
| 15 |
Solution of the open string motion in the light-cone gauge |
Sections 9.2-9.4 |
| 16 |
Light-cone fields and particles |
Sections 9.5-10.1 |
| 17 |
Light-cone fields and particles (cont.) |
Sections 10.2-10.4 |
| 18 |
Open strings |
|
| 19 |
Critical dimension
Constructing the state space
Tachyons
|
|
| 20 |
Closed strings |
|
| 21 |
Wrap-up of closed strings
Superstrings
|
|
| |
Test 2 |
|
| 22 |
Superstrings (cont.) |
|
| 23 |
Closed strings
Heterotic string theory
|
|
| 24 |
Dp-branes
Parallel Dp's
|
|
| 25 |
Dp-branes (cont.) |
|
| 26 |
Final exam review |
|
| |
Final exam week |
|
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