Methods of Quantization

2001

Schweiger, Wolfgang , Latal, Heimo , Internationale Universitatswochen Fur Kern- Und Teilchenphysik 2000 s (COR) 저자(글)

Springer · 2001년 07월 17일

책 소개

작가정보

저자(글) Schweiger, Wolfgang

저자(글) Latal, Heimo

저자(글) Internationale Universitatswochen Fur Kern- Und Teilchenphysik 2000 s (COR)

목차

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

기본정보

ISBN	9783540421009 ( 3540421009 )
발행(출시)일자	2001년 07월 17일
쪽수	228쪽
크기	156 * 234 * 14 mm / 517 g
총권수	1권
언어	영어