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Preface | ||
1 | Micro and Macro Physics | 1 |
1.1 | Micro, Macro, and Thermal | 1 |
1.2 | Classical Physics for Particles and Fields | 3 |
1.3 | Quantum Mechanics and Quantum Field Theory | 8 |
1.4 | The c-q Transmutation Condition | 12 |
1.5 | Matter and the Vacuum | 13 |
2 | Vacuum Correlation | 15 |
2.1 | Number Representation | 15 |
2.2 | Coherent, Squeezed or Thermal-Like States | 16 |
2.2.1 | Coherent States | 16 |
2.2.2 | Squeezed States | 19 |
2.2.3 | Two-Mode Squeezed States | 21 |
2.2.4 | An Equivalence Theorem | 23 |
2.3 | Noise in Pure States | 24 |
2.3.1 | Thermal-Like Noise in the Two-Mode State | 24 |
2.3.2 | Correlation through the Vacuum | 26 |
2.4 | Pure State and Mixed State | 28 |
2.4.1 | Bosonic System | 28 |
2.4.2 | Thermal Vacuum for Fermionic Oscillators | 30 |
2.4.3 | Non-Trivial Parameters in Vacua | 32 |
2.5 | TFD Mechanism for Noise Creation | 33 |
2.6 | TFD Mechanism and Black Hole | 34 |
2.7 | Phase and Time Operators in TFD | 35 |
3 | Inequivalent Vacua | 39 |
3.1.1 | Infrared Catastrophe of Bremsstrahlung | 39 |
3.1.2 | Vacuum Polarization | 40 |
3.1.3 | Renormalization | 42 |
3.2 | Many Vacua | 42 |
3.3 | Anomalous Operators | 45 |
3.4 | Pure State and Mixed State | 46 |
3.4.1 | Bosonic Systems | 46 |
3.4.2 | Fermionic Systems | 47 |
4 | Quasi-Particle Picture | 50 |
4.1 | Modern Particle Picture and the Old Atomism | 50 |
4.2 | Countably Infinite Degrees of Freedom | 50 |
4.3 | Continuous Set of Number States | 52 |
4.4 | Quasi-Particles and Dynamical Map | 52 |
4.5 | Time-Independent Global Operators | 55 |
4.6 | The Dynamical Map of the Hamiltonian | 57 |
4.6.1 | Quasi-Particle Free Hamiltonian | 57 |
4.6.2 | Reactions among Quasi-Particles | 59 |
4.6.3 | Asymptotic Fields and Quasi-Particles | 59 |
4.6.4 | Many Choices for Incoming Particles | 61 |
4.6.5 | Renormalization | 62 |
5 | Ordered States | 64 |
5.1 | Spontaneously Broken Symmetries | 64 |
5.1.1 | A Physical Picture | 64 |
5.1.2 | A Mathematical Picture | 65 |
5.1.3 | Symmetry Rearrangement | 67 |
5.1.4 | Boson Transformation | 68 |
5.1.5 | Low Energy Theorem I | 69 |
5.1.6 | Generators and the Nother Current | 69 |
5.1.7 | The Ward-Takahashi Relations | 70 |
5.1.8 | [Theta]-Selection | 71 |
5.1.9 | Summary of this Section | 73 |
5.2 | Broken Phase Symmetry in a Scalar Model | 74 |
5.2.2 | Model | 74 |
5.2.3 | The Nother Current and the Generator | 74 |
5.2.4 | Phase Symmetry Rearrangement | 75 |
5.2.5 | The Order Parameter and [Theta]-Selection | 75 |
5.2.6 | The Dynamical Map of the Current | 76 |
5.2.7 | A Fluctuation Effect | 76 |
5.2.8 | A Strategy for Computational Analysis | 78 |
5.2.9 | Superfluid Current | 79 |
5.3 | Superconductivity | 79 |
5.3.2 | The BCS Model | 80 |
5.3.3 | The Current and the Generator | 81 |
5.3.4 | Phase Symmetry Rearrangement | 81 |
5.3.5 | The Dynamical Map of Charge Density | 82 |
5.3.6 | The Nambu-Goldestone Field | 82 |
5.3.7 | Are NG-Bosons Entirely Eliminated? | 83 |
5.3.8 | Order Parameter and [Theta]-Selection | 84 |
5.3.9 | A Fluctuation Effect | 85 |
5.3.10 | Gauge Invariance | 86 |
5.3.11 | A Strategy in Computational Analysis | 87 |
5.4 | Non-Abelian Symmetry Breakdown | 88 |
5.4.1 | Spontaneously Broken Spin Symmetry | 88 |
5.4.2 | Symmetry Rearrangement | 91 |
5.4.3 | Low Energy Theorem II | 92 |
5.5 | c-q Transmutation and Crystal Phonon | 93 |
5.6 | The Spontaneous Creation of Mass | 95 |
6 | Macroscopic Objects | 99 |
6.1 | Boson Transformation | 99 |
6.1.2 | Planck's Constant | 99 |
6.1.3 | Boson Transformation | 100 |
6.1.4 | Induced Potential and Zero-Energy Mode | 102 |
6.1.5 | Quantum Mechanical Operators | 105 |
6.1.6 |
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