文档介绍：TABLE OF CONTENTS
Introduction I
I. Lattice Gauge Theories 3
I. The Scheme of Lattice Gauge Theories 4
2. Fundamental Properties 12
a) Osterwalder-Schrader Positivity and Consequences 12
b) Some Observables and Their Meaning 16
c) "ic" Inequality 22
d) Correlation Inequalities 28
3. Expansion Methods 29
a) General Algebraic Formalism for Polymers 31
b) Application of the Formalism to Lattice Gauge Theories : Convergence 38
c) Results : Concequences of Cluster Expansion Convergence 47
4. Further Developments 66
a) Abelian Higgs Models in Two Dimensions : 0-Vacua, Phase Transitions 67
and Confinement of Fractional Charges
b) The Three-Dimensional Abelian Higgs Model : Phase Structure 71
c) Guth's Theorem : Existence of a Non-confining (Coulombic)' Phase in
the Four-Dimensional U(1)-Model 74
d) SU(n) Confines if ~ Does
n 86
e) The Interplay of Electric and ic Properties in the Confinement
Problem 88
f) Some Rough Ideas about Roughening 97
II. Continuum Gauge Quantum Field Theories 99
5. Approaches to the Construction of Continuum Gauge Quantum Field Theories 99
a) The Scaling Limit 99
b) Direct Continuum Constructions 103
6. Convergence to the Continuum Limit in External or Cutoff Gauge Fields iii
a) Convergence of Green's Functions iii
b) Convergence of Determinants I18
c) Convergence of States (Expectation Values) in External Gauge Fields 125
d) Convergence of Expectations in Fully Quantized Theories with Cutoff
on the Gauge Field 130
IV
7. Removal of All Cutoffs, Verification of Axioms in Two Dimensions 133
a) The Stability Expansion 133
b) Volume Dependent and Volume Independent Bounds 142
c) Thermodynamic Limit; Verification of the Axioms 152
8. A Framework for Non-local Gauge Invariant Objects 163
a) Assumptions 164
b) Reconstruction of a Relativistic Quantum Mechanics 167
c) "Wightman Functions" and their Analytieity 175
d) Boundary Values