Quantum Time & History

Table of Contents

Part 1: Basic Mathematical Structure

1. Hilbert Space and Inner Product, Operator Theory
2. Composition and States of Quantum Systems: Tensor Product, Density Matrix, Partial Trace
3. Symmetry, Group (Group), and Generators (Generators)

Part 2: Dynamics and Paths

4. Action Functional and Variation, Euler–Lagrange Equations
5. Path Integral Axiomatization, Functional Integral Notation 𝓓x

Part 3: Quantum Information and Entanglement

6. Dynamics of Open Quantum Systems: Quantum Channels and Representations
7. Consistent Histories and Quantum Probability
8. Delayed Choice and Quantum Eraser: How Later Choices Determine Present Statistics
9. Quantum Darwinism: How Objective Reality Emerges

Part 4: Time, Causality, and Reality

10. Emergent Time: The Flow of Time in a Static Universe (Page–Wootters)
11. C*·von Neumann Operator Algebra (Thermal Time)
12. Uncertain Causality Order: When ‘Before’ and ‘After’ Become Superposed
13. Leggett–Garg Inequality: Hidden Quantumness Within Time

Appendix

• Appendix 1: Linear Algebra Basics for Quantum Mechanics
• Appendix 2: Classical Probability and Quantum Probability
• Appendix 3: Notation Guide
• Appendix 4: Group Classification System
• Appendix 5: Core Learning Roadmap and Strategy
• Appendix 6: This Book’s Topology and Next Steps