CONTENTS
PREFACE TO THE SERIES
Vlll
PREFACE
IX
CHAPTER 1 STATISTICAL MECHANICS AND
QUANTUM FIELD THEORY
1
1.1 Quantum Particles
1
1.2 Global and Local Symmetries.
Preliminary Description
4
1.3 Discrete Global Symmetries
5
1.4 Continuum Abelian Global Symmetries
11
1.5 Non-Abelian Global Symmetries
13
1.6 Discrete Gauge Symmetries
14
1.7 0(2) Gauge Systems
15
1.8 Non-Abelian Gauge Theories
17
CHAPTER 2 ASYMPTOTIC FREEDOM AND THE
RENORMALIZATION GROUP
19
2.1 Principal Chiral Fields
19
2.2 The n-Fields
27
2.3 Non-Abelian Gauge Fields for ^ = 4
29
CHAPTER 3 THE STRONG COUPLING
EXPANSION
3.1 Ising Model
3.2 Continuous Global Symmetry
3.3 Gauge Symmetries
33
34
37
40
CHAPTER 4 INSTANTONS IN ABELIAN SYSTEMS
49
4.1 Instantons in Quantum Mechanics and the
Ising model
49
4.2 Instantons in the Global 0(2) Model
54
4.3 Compact QED (0(2) Gauge Model)
62