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Tables of Contents for Methods of Quantization
Chapter/Section Title
Page #
Page Count
Forms of Relativistic Dynamics
1
54
Bernard L. G. Bakker
Introduction
1
2
The Poincare Group
3
1
Forms of Relativistic Dynamics
4
5
Comparison of Instant Form, Front Form, and Point Form
6
3
Light-Front Dynamics
9
10
Relative Momentum, Invariant Mass
9
5
The Box Diagram
14
5
Poincare Generators in Field Theory
19
4
Fermions Interacting with a Scalar Field
20
1
Instant Form
20
1
Front Form (LF)
21
1
Interacting and Non-interacting Generators on an Instant and on the Light Front
22
1
Light-Front Perturbation Theory
23
4
Connection of Covariant Amplitudes to Light-Front Amplitudes
24
2
Regularization
26
1
Minus Regularization
26
1
Triangle Diagram in Yukawa Theory
27
10
Covariant Calculation
28
2
Construction of the Current in LFD
30
7
Numerical Results
37
1
Four Variations on a Theme in φ3 Theory
37
14
Covariant Calculation
39
3
Instant-Form Calculation
42
5
Calculation in Light-Front Coordinates
47
2
Front-Form Calculation
49
2
Dimensional Regularization: Basic Formulae
51
1
Four-Dimensional Integration
52
1
Some Useful Integrals
53
2
References
53
2
Light-Cone Quantization: Foundations and Applications
55
88
Thomas Heinzl
Introduction
55
3
Relativistic Particle Dynamics
58
16
The Free Relativistic Point Particle
58
6
Dirac's Forms of Relativistic Dynamics
64
4
The Front Form
68
6
Light-Cone Quantization of Fields
74
24
Construction of the Poincare Generators
74
2
Schwinger's (Quantum) Action Principle
76
2
Quantization as an Initial- and/or Boundary-Value Problem
78
6
DLCQ-Basics
84
4
DLCQ-Causality
88
6
The Functional Schrodinger Picture
94
2
The Light-Cone Vacuum
96
2
Light-Cone Wave Functions
98
15
Kinematics
99
2
Definition of Light-Cone Wave Functions
101
3
Properties of Light-Cone Wave Functions
104
1
Examples of Light-Cone Wave Functions
105
8
The Pion Wave Function in the NJL Model
113
23
A Primer on Spontaneous Chiral Symmetry Breaking
114
3
NJL Folklore
117
4
Schwinger-Dyson Approach
121
6
Observables
127
9
Conclusions
136
7
References
138
5
Quantization of Constrained Systems
143
40
John R. Klauder
Introduction
143
5
Initial Comments
143
1
Classical Background
144
1
Quantization First: Standard Operator Quantization
145
1
Reduction First: Standard Path Integral Quantization
146
1
Quantization First ≢ Reduction First
147
1
Outline of the Remaining Sections
148
1
Overview of the Projection Operator Approach to Constrained System Quantization
148
4
Coherent States
148
1
Constraints
149
1
Dynamics for First-Class Systems
150
1
Zero in the Continuous Spectrum
151
1
Alternative View of Continuous Zeros
152
1
Coherent State Path Integrals Without Gauge Fixing
152
6
Enforcing the Quantum Constraints
153
1
Reproducing Kernel Hilbert Spaces
154
1
Reduction of the Reproducing Kernel
155
1
Single Regularized Constraints
156
1
Basic First-Class Constraint Example
157
1
Application to General Constraints
158
10
Classical Considerations
158
2
Quantum Considerations
160
2
Universal Procedure to Generate Single Regularized Constraints
162
2
Basic Second-Class Constraint Example
164
1
Conversion Method
165
1
Equivalent Representations
166
1
Equivalence of Criteria for Second-Class Constraints
167
1
Selected Examples of First-Class Constraints
168
8
General Configuration Space Geometry
168
2
Finite-Dimensional Hilbert Space Examples
170
2
Helix Model
172
1
Reparameterization Invariant Dynamics
173
2
Elevating the Lagrange Multiplier to an Additional Dynamical Variable
175
1
Special Applications
176
4
Algebraically Inequivalent Constraints
176
2
Irregular Constraints
178
2
Some Other Applications of the Projection Operator Approach
180
3
References
181
2
Algebraic Methods of Renormalization
183
24
Klaus Sibold
Generalities
183
7
Renormalization Schemes
183
3
The Action Principle
186
3
Green Functions and Operators
189
1
The Quantization of Gauge Theories
190
7
The Abelian Case
190
2
BRS Transformations
192
2
The Slavnov-Taylor Identity
194
3
Applications
197
10
The Electroweak Standard Model
197
4
Supersymmetry in Non-linear Realization
201
1
Susy Gauge Theories
202
3
References
205
2
Functional Integrals for Quantum Theory
207
16
Ludwig Streit
Introduction
207
1
White Noise Analysis
208
5
Smooth and Generalized Functionals
210
1
Characterization of Generalized Functionals Φ ε (S)*
210
2
Calculus
212
1
Quantum Field Theory
213
3
The Vacuum Density
213
1
Dynamics in Terms of the Vacuum
214
2
Feynman Integrals
216
7
The Interactions
218
2
The Morse Potential
220
1
References
221
2
Seminars
223