Five Lectures on Supersymmetry (FLS)

Cover......Page 1
Contents......Page 5
Preface......Page 7
Introduction......Page 8
Lecture 1. What Are Fermions?......Page 11
Fermions in Quantum Mechanics......Page 12
Superalgebra......Page 16
A brief return to quantum particles......Page 21
Classical particles and their quantization......Page 22
Spaces with anticommuting functions......Page 25
From classical to quantum......Page 29
Lecture 2. Lagrangians and Symmetries......Page 31
Some differential geometric preliminaries......Page 32
Lagrangian field theory......Page 33
Symmetries and Noether currents......Page 39
Examples of symmetries in mechanics......Page 42
Superspacetime and manifest supersymmetry......Page 47
Quantization of the superparticle......Page 49
Yet another word about signs......Page 50
Lecture 3. Supersymmetry in Various Dimensions......Page 52
Spinors on Minkowski spacetime......Page 53
Superspacetime and the super Poincaré group......Page 55
Central extensions and R-symmetry......Page 59
Representations of the super Poincaré group......Page 61
A quick tour of fields and classical field theories......Page 65
From classical fields to quantum particles......Page 68
Lecture 4. Theories with Two Supersymmetries......Page 74
σ-models and gauge theories ......Page 75
The superspacetime M^(3/2 )......Page 78
Supersymmetric σ-model in 3 dimensions......Page 80
A supersymmetric potential ......Page 84
Dimensional reduction to n = 2 dimensions......Page 86
Dimensional reduction to n = 1......Page 89
Gauge theory on M^(3/2)......Page 90
Lecture 5. Theories with More Supersymmetry......Page 92
Fundamental vs. effective lagrangians......Page 93
Dimensional reduction of gauge fields......Page 95
Quantum particles in n = 4 dimensions......Page 96
The superspacetime M^(4/4)......Page 98
Supersymmetric σ-model on M^(4/4)......Page 99
The superpotential......Page 101
Gauge theory on M^(4/4)......Page 102
The general theory on M^(4/4)......Page 103
Dimensional reductions of theories with s = 3 and s = 4 supersymmetries......Page 105
Theories with s = 8 supersymmetries......Page 109
Theories with s = 16 supersymmetries......Page 112
References......Page 117
Index......Page 120