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 String Theory for Undergraduates  posted by  member7_php   on 2/13/2009 Add To Favorites
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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 BY-NC-SA

### 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.

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.

ACTIVITIES PERCENTAGES
Homework 35%
Test 1 20%
Test 2 20%
Final exam 25%

## 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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