 
Abstract/Syllabus:

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 BYNCSA
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 MTheory: 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
Lightcone 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: NambuGoto 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 sigmaparametrization
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 lightcone gauge 

16 
Lightcone fields and particles 

17 
Lightcone 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 
Wrapup of closed strings
Superstrings



Test 2 

22 
Superstrings (cont.) 

23 
Closed strings
Heterotic string theory


24 
Dpbranes
Parallel Dp's

Homework 11 due 
25 
Dpbranes (cont.) 

26 
Final exam review 


Final exam week 




Further Reading:

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 MTheory: A Modern Introduction. Cambridge, UK: Cambridge University Press, 2007. ISBN: 9780521860697.
Course readings.
SES # 
TOPICS 
READINGS 
1 
Announcements, introduction
Lorentz transformations
Lightcone coordinates

Sections 2.12.3 
2 
Energy and momentum
Compact dimensions, orbifolds
Quantum mechanics and the square well

Sections 2.42.9 
3 
Relativistic electrodynamics
Gauss' law
Gravitation and Planck's length

Sections 3.13.6 
4 
Gravitational potentials, compactification, and large extra dimensions 
Sections 3.73.10 
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: NambuGoto action, equations of motion and boundary conditions 
Sections 6.16.5 
11 
Static gauge, transverse velocity, and string action
Motion of free open string endpoints

Sections 6.66.9 
12 
The sigmaparametrization
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 8.48.6, 9.1 
15 
Solution of the open string motion in the lightcone gauge 
Sections 9.29.4 
16 
Lightcone fields and particles 
Sections 9.510.1 
17 
Lightcone fields and particles (cont.) 
Sections 10.210.4 
18 
Open strings 

19 
Critical dimension
Constructing the state space
Tachyons


20 
Closed strings 

21 
Wrapup of closed strings
Superstrings



Test 2 

22 
Superstrings (cont.) 

23 
Closed strings
Heterotic string theory


24 
Dpbranes
Parallel Dp's


25 
Dpbranes (cont.) 

26 
Final exam review 


Final exam week 

12 
The sigmaparametrization
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 8.48.6, 9.1 
15 
Solution of the open string motion in the lightcone gauge 
Sections 9.29.4 
16 
Lightcone fields and particles 
Sections 9.510.1 
17 
Lightcone fields and particles (cont.) 
Sections 10.210.4 
18 
Open strings 

19 
Critical dimension
Constructing the state space
Tachyons


20 
Closed strings 

21 
Wrapup of closed strings
Superstrings



Test 2 

22 
Superstrings (cont.) 

23 
Closed strings
Heterotic string theory


24 
Dpbranes
Parallel Dp's


25 
Dpbranes (cont.) 

26 
Final exam review 


Final exam week 




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