ISBN: 3-540-66517-X
TITLE: Information Theory and Quantum Physics
AUTHOR: Green, Herbert S.
TOC:

1. First Principles 1
1.1 Relativity and Equivalence 1
1.2 Action 3
1.3 Information and Probability 7
1.4 Uncertainty and Indeterminacy 11
2. Quantal Bits 15
2.1 Creation and Annihilation 20
2.2 Classical Geometry on a Sphere 22
2.3 Spin and Rotation 23
2.3.1 The Group of Rotations 25
2.4 Lorentz Transformations 26
2.5 Translations in Space and Time 29
2.6 Elementary String Theory 32
2.7 Summary 34
3. Events in Space and Time 37
3.1 Projective Geometries 41
3.2 Classical Geometry of Space-Time 43
3.3 Changes of Observational Frame 46
3.4 Events as Quantal Information 48
3.4.1 Spin of the Photon 50
3.5 Fermions in Space-Time 51
3.5.1 Dirac's Equation 54
3.5.2 Charged and Neutral Particles 57
3.6 Summary 58
4. Quantal `Tapes' 61
4.1 Representation of States of Higher Spin 63
4.1.1 `Tapes' for Particles of Higher Spin 65
4.1.2 Matrices for Higher Spin 67
4.1.3 Spin 0 and 1 68
4.2 Maxwell's Equations and the Photon 71
4.3 Systems of Fermions 73
4.4 Bosons 75
4.4.1 The Factorization Technique 76
4.4.2 The Tape Constructed from Qubits 77
4.4.3 Systems of Bosons 79
4.5 Observables with Continuous Spectra 79
4.5.1 Quasi-continuous Spectra 80
4.6 Summary 81
5. Observables and Information 83
5.1 Relativistic and Non-relativistic Approximations 86
5.1.1 Orbital Angular Momentum 87
5.2 Non-relativistic Quantum Mechanics 88
5.2.1 The Hydrogen Atom 89
5.2.2 Scattering and the S-Matrix 92
5.3 Uncertainty Relations 94
5.4 Special Relativistic Quantum Mechanics 96
5.4.1 Elastic Scattering 98
5.5 Selected and Unselected Observables 100
5.6 The Fundamental Observables of Physics 102
5.6.1 Schrdinger's Wave Mechanics 103
5.6.2 The Heisenberg Representation. 104
5.6.3 The Interaction Representation 105
5.7 Statistical Physics 106
5.7.1 Macroscopic and Microscopic Variables 108
5.8 Theory of Electrolytes 110
5.8.1 The DebyeHckel Equation 112
5.9 Summary 113
6. Quantized Field Theories 115
6.1 Free Field Theories 119
6.1.1 Spin 1/2 122
6.1.2 Spin 0 124
6.1.3 Spin 1 127
6.2 Interacting Fields 129
6.2.1 The S-Matrix 132
6.2.2 Ordering in Time 134
6.3 Quantum Electrodynamics 136
6.4 Gauge Groups and String Theories 142
6.4.1 String Theories 143
7. Gravitation 145
7.1 Geometry in Terms of Quantal Information 148
7.1.1 The Relativistic Density Matrix 150
7.1.2 Representations for Arbitrary Spin 151
7.2 Quantum Geometry 153
7.2.1 The Curvature of Space-Time 155
7.3 Einstein's Gravitational Field Equations 158
7.3.1 Classical Embedding of Schwarzschild's Solution 158
7.3.2 More General Solutions of Einstein's Equations 161
7.3.3 Lagrangian Densities 162
7.4 Quantal Embedding 163
7.5 Gauge Theories with Gravitation 167
7.6 Summary 169
8. Measurement and the Observer 171
8.1 Detectors and Measuring Devices 173
8.1.1 Theory of Measurement 177
8.2 Qubits of Fluctuating Electrolytic Potentials 181
8.2.1 The Cortex as a Quantal Turing Machine 182
8.2.2 The Qubits of Potential Fluctuations in an Electrolyte 183
8.2.3 Transmission of Information Across the Cellular Membrane 186
8.3 Cells and Membranes 193
8.3.1 Graded and Action Potentials 196
8.4 The Animal Cortex 199
8.4.1 Organization of Cells in Columns and Zones 199
8.4.2 The Subdivisions and Functions of the Cortex 199
8.5 Theory of Consciousness. 202
8.6 Consciousness in Nature 206
A. Appendix: Matrices. 211
A.1 Definitions and Elementary Properties 211
A.1.1 Direct Products and Vector Subscripts 213
A.1.2 The Imaginary Unit as a Matrix 214
A.2 Determinants 215
A.3 Eigenvalues of Matrices 217
A.3.1 Reduction of a Finite Matrix to Spectral Form 219
A.3.2 Representation of Observables by Matrices 220
A.4 The Factorization Method 221
A.5 Continuous Eigenvalues 223
A.6 Parafermion Representations of Lie Algebras 225
A.6.1 Invariants and Representations of so(2N + 1) 228
Bibliography 231
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