| 1 |
Announcements, Introduction
Lorentz Transformations |
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| 2 |
Light-cone Coordinates, Energy and Momentum |
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| 3 |
Compact Extra Dimensions and Orbifolds
Square Well with Extra Dimension
Relativistic Formulation of Maxwell's Equations |
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| 4 |
Electric Fields in Higher Dimensions
Planckian Units
Gravitational Constants and Compactification |
Homework 1 due |
| 5 |
Large Extra Dimensions
Nonrelativistic Strings and Lagrangian Mechanics |
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| 6 |
Nonrelativistic String Lagrangian
The Relativistic Point Particle: Action, Reparametrization Invariance and Equations of Motion |
Homework 2 due |
| 7 |
Relativistic Strings: Area Functional, Nambu-Goto Action, Equations of Motion and Boundary Conditions |
Homework 3 due |
| 8 |
Comments on Schwartz Inequality in a Two-dimensional Minkowski Space
Static Gauge, Transverse Velocity and String Action
Motion of Free Open String Endpoints |
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| 9 |
The σ-Parameterization using the Energy carried by the String
Equations of Motion for Free Open Strings |
Homework 4 due four days after lecture 9 |
| 10 |
Circular Motion of an Open String
Periodicity Conditions for the Motion of Closed Strings
The Formation of Cusps
Conserved Currents in E&M
Conserved Charges in Lagrangian Mechanics |
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| 11 |
Conserved Charges in Lagrangian Field Theory
Momentum Charges for the String
Lorentz Charges for the Strings
Angular Momentum of the Rotating String |
Homework 5 due four days after lecture 11 |
| 12 |
Discuss α´ and the String Length /s
Begin Chapter 9 - General Gauges: Fixing τ and Natural Units
Associated σ-Parameterization of Open and Closed Strings |
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Test 1 |
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| 13 |
Discuss Test
Finish Chapter 9 - Constraints, Wave Equations, and Mode Expansions
Light-cone Solution of the Equations of Motion |
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| 14 |
Light-cone Fields and Particles
An Action for Scalar Fields
Classical Plane-wave Solutions
Quantum Scalar Fields and Particle States |
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| 15 |
Photon States
Classical Motion of the Particle in the Light-cone Gauge
The Schroedinger and Heisenberg Pictures |
Homework 6 due one day after lecture 15 |
| 16 |
Quantization of the Point Particle
Quantum Particle and Scalar Particles
Light-cone Momentum Generators
Light-cone Lorentz Generators |
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| 17 |
Relativistic Quantum Open Strings |
Homework 7 due one day after lecture 17 |
| 18 |
Relativistic Quantum Open Strings (cont.)
Relativistic Quantum Closed Strings |
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| 19 |
Relativistic Quantum Closed Strings (cont.) |
Homework 8 due one day after lecture 19 |
| 20 |
Dp-branes and Boundary Conditions
Quantizing Open Strings on Dp-branes
Open Strings between Parallel Dp-branes
Strings between Parallel Dp- and Dq-branes |
Homework 9 due four days after lecture 20 |
| 21 |
Fundamental String Charge
Visualizing String Charge
Strings Ending on D-branes |
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| 22 |
T-duality of Closed Strings |
Homework 10 due four days after lecture 22 |
| 23 |
T-duality of Closed Strings (cont.) |
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Test 2 |
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| 24 |
Electromagnetic Fields on D-branes |
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| 25 |
Nonlinear and Born-Infeld Electrodynamics |
Project due |