دانلود کتاب Phase Space Picture of Quantum Mechanics: Group Theoretical Approach

فهرست مطالب :

Preface Introduction 1 PHASE SPACE IN CLASSICAL MECHANICS 1.1 Hamiltonian Form of Classical Mechanics 1.2 Trajectories in Phase Space .. 1.3 Canonical Transformations . . . . . . . . 6 1.4 Coupled Harmonic Oscillators . . . . . . . 9 1.5 Group of Linear Canonical Transformations in Four~ Dimensional Phase Space . . . . . . . . . . . . . 12 1.6 Poisson Brackets . . . . . . . 14 1.7 Distributions in Phase Space 15 2 FORMS OF QUANTUM MECHANICS 2.1 Schrodinger and Heisenberg Pictures . . . 2.2 Interaction Representation . . . . . . . . . 2.3 Density~Matrix Formulation of Quantum 2.4 Mixed States . . . . . . . . . . . . . . . 2.5 Density Matrix and Ensemble Average . 2.6 Time Dependence of the Density Matrix Mechanics 3 WIGNER PHASE-SPACE DISTRIBUTION FUNCTIONS 37 3.1 Basic Properties of the Wigner Phase~Space Distribution Function 38 3.2 Time Dependence of the Wigner Function 40 3.3 Wave Packet Spreads . 42 3.4 Harmonic Oscillators . 45 3.5 Density Matrix . . . . 47 3.6 Measurable Quantities 3. 7 Early and Recent Applications 4 LINEAR CANONICAL TRANSFORMATIONS IN QUANTUM MECHANICS 57 4.1 Canonical Transformations in Two-Dimensional Phase Space 57 4.2 Linear Canonical Transformations in Quantum Mechanics . . 60 4.3 Wave Packet Spreads in Terms of Canonical Transformations 63 4.4 Harmonic Oscillators . . . . . . . . . . . . . . . . . . . . . . . 64 4.5 (2 + I)-Dimensional Lorentz Group . . . . . . . . . . . . . . 66 4.6 Canonical Transformations in Four-Dimensional Phase Space 69 4.7 The Schrodinger Picture of Two-Mode Canonical Transformations 72 4.8 (3 + 2)-Dimensional de Sitter Group . . . . . . . . . . . . . . . . . 73 5 COHERENT AND SQUEEZED STATES 5.1 Phase-Number Uncertainty Relation 5.2 Baker-Campbell-Hausdorff Relation 5.3 Coherent States of Light . . . . . . . 5.4 Symmetry Groups of Coherent States 5.5 Squeezed States . . . . . . . . . . . . . 5.6 Two-Mode Squeezed States ..... . 5.7 Density Matrix through Two-Mode Squeezed States 6 PHASE-SPACE PICTURE OF COHERENT AND SQUEEZED STATES 99 6.1 Invariant Subgroups . . . . . 100 6.2 Coherent States . . . . . . . . 102 6.3 Single-Mode Squeezed States 105 6.4 Squeezed Vacuum ...... . 6.5 Expectation Values in terms of Vacuum Expectation Values 6.6 Overlapping Distribution Functions . 6. 7 Thomas Effect . . . . . . . 6.8 Two-Mode Squeezed States 6.9 Contraction of Phase Space 7 LORENTZ TRANSFORMATIONS 7.1 Group of Lorentz Transformations . 7.2 Little Groups of the Lorentz Group . 7.3 Massless Particles .......... . 7.4 Decomposition of Lorentz Transformations. 129 7.5 Analytic Continuation to the Little Groups for Massless and Imaginary- Mass particles . . . . . . . . . . 131 7.6 Light-Cone Coordinate System . . . . 133 7.7 Localized Light Waves ........ . 7.8 Covariant Localization of Light Waves 7.9 Covariant Phase-Space Picture of Localized Light Waves . 7.10 Uncertainty Relations for Light Waves and for Photons 8 COVARIANT HARMONIC OSCILLATORS 8.1 Theory of the Poincare Group . . . . . . . . . . 8.2 Covariant Harmonic Oscillators . . . . . . . . . . . . . . . . 8.3 Irreducible Unitary Representations of the Poincare Group 8.4 C-number Time-Energy Uncertainty Relation ..... . 8.5 Dirac's Form of Relativistic Theory of "Atom" . . . . 157 8.6 Lorentz Transformations of Harmonic Oscillator Wave functions. 160 8.7 Covariant Phase-Space Picture of Harmonic Oscillators. 162 9 LORENTZ-SQUEEZED HADRONS 9.1 Quark Model ............ . 9.2 Hadronic Mass Spectra . . . . . . . . 9.3 Hadrons in the Relativistic Quark Model. 9.4 Form Factors of Nucleons ........ . 9.5 Phase-Space Picture of Overlapping Wave Functions 9.6 Feynman's Parton Picture . . . . . . . . . . . . . . . . 9.7 Experimental Observation of the Parton Distribution . 10 SPACE-TIME GEOMETRY OF EXTENDED PARTICLES 193 10.1 Two-Dimensional Euclidean Group and Cylindrical Group 195 10.2 Contractions of the Three-Dimensional Rotation Group 197 10.3 Three-Dimensional Geometry of the Little Groups . 200 10.4 Little Groups in the Light-Cone Coordinate System 202 10.5 Cylindrical Group and Gauge Transformations . . . 204 10.6 Little Groups for Relativistic Extended Particles . . 207 10.7 Lorentz Transformations and Hadronic Temperature 210 10.8 Decoherence and Entropy . . . . . . . . . . . . . . . . 213 A Reprinted Articles 217 A.1 E.P. Wigner, On the Quantum Correction for Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 A.2 E.P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 A.3 P.A.M. Dirac, Unitary Representations of the Lorentz Group . . 293 A.4 P.A.M. Dirac, A Remarkable Representation of the 3 + 2 de Sitter Group ................................... 307 References Index