Contents -- Preface -- Acknowledgments -- 1. Introduction -- 1.1 Soft Introduction to Quantum Mechanics -- 1.2 Hilbert Space -- 1.2.1 Quantum Hilbert Space -- 1.2.2 Formal Hilbert Space -- 1.3 Human Intelligence, Mind and Reason -- 1.3.0.1 Human Reason -- 2. Elements of Quantum Mechanics -- 2.1 Basics of Non-Relativistic Quantum Mechanics -- 2.1.1 Canonical Quantization -- 2.1.2 Quantum States and Operators -- 2.1.3 Quantum Pictures -- 2.1.4 Spectrum of a Quantum Operator -- 2.1.5 General Representation Model -- 2.1.6 Direct Product Space -- 2.1.7 State-Space for n Quantum Particles -- 2.2 Relativistic Quantum Mechanics and Electrodynamics -- 2.2.1 Difficulties of the Relativistic Quantum Mechanics -- 2.2.2 Particles of Half-Odd Integral Spin -- 2.2.3 Particles of Integral Spin -- 2.2.4 Dirac's Electrodynamics Action Principle -- 2.2.5 Dirac Equation and Formal QED in Brief -- 2.2.6 Lorentzian Space-Time and Gravity -- 2.2.7 Unification of Fundamental Interactions -- 2.2.7.1 First Unification -- 3. Feynman Path Integrals -- 3.1 Path Integrals: Sums Over Histories -- 3.1.1 Intuition Behind a Path Integral -- 3.1.1.1 Classical Probability Concept -- 3.1.1.2 Quantum Probability Concept -- 3.1.1.3 Quantum Coherent States -- 3.1.1.4 Dirac's hbra

3.1.4 Statistical Mechanics via Path Integrals -- 3.1.5 Path-Integral Monte-Carlo Simulation -- 3.1.6 Sum over Geometries and Topologies -- 3.1.6.1 Simplicial Quantum Geometry -- 3.1.6.2 Discrete Gravitational Path Integrals -- 3.1.6.3 Regge Calculus -- 3.1.6.4 Lorentzian Path Integral -- 3.2 Dynamics of Quantum Fields -- 3.2.1 Path Integrals and Green's Functions -- 3.2.2 Topological Quantum Field Theory -- 3.2.3 TQFT and Seiberg-Witten Theory -- 3.2.3.1 SW Invariants and Monopole Equations -- 3.2.3.2 Topological Lagrangian -- 3.2.3.3 Quantum Field Theory -- 3.2.3.4 Dimensional Reduction and 3D Field Theory -- 3.2.3.5 Geometrical Interpretation -- 3.2.4 TQFTs Associated with SW-Monopoles -- 3.2.4.1 Dimensional Reduction -- 3.2.4.2 TQFTs of 3D Monopoles -- 3.2.4.3 Non-Abelian Case -- 3.3 Stringy Geometrodynamics -- 3.3.1 Stringy Actions and Amplitudes -- 3.3.1.1 Strings -- 3.3.1.2 Interactions -- 3.3.1.3 Loop Topology of Closed Surfaces -- 3.3.2 Transition Amplitudes for Strings -- 3.3.3 Weyl Invariance and Vertex Operator Formulation -- 3.3.4 More General Stringy Actions -- 3.3.5 Transition Amplitude for a Single Point Particle -- 3.3.6 Witten's Open String Field Theory -- 3.3.6.1 Operator Formulation of String Field Theory -- 3.3.6.2 Open Strings -- 3.3.6.3 Construction of Overlap Vertices -- 3.3.6.4 Transformation of String Fields -- 3.3.7 Topological Strings -- 3.3.8 Geometrical Transitions -- 3.3.9 Topological Strings and Black Hole Attractors -- 3.4 Non-Quantum Applications of Path Integrals -- 3.4.1 Stochastic Optimal Control -- 3.4.1.1 Path-Integral Formalism -- 3.4.1.2 Monte Carlo Sampling -- 3.4.2 Nonlinear Dynamics of Option Pricing -- 3.4.2.1 Theory and Simulations of Option Pricing -- 3.4.2.2 Option Pricing via Path Integrals -- 3.4.2.3 Continuum Limit and American Options -- 3.4.3 Dynamics of Complex Networks.

3.4.3.1 Continuum Limit of the Kuramoto Net -- 3.4.3.2 Path-Integral for Complex Networks -- 3.4.4 Cerebellum as a Neural Path-Integral -- 3.4.4.1 Spinal Autogenetic Reflex Control -- 3.4.4.2 Cerebellum - the Comparator -- 3.4.4.3 Hamiltonian Action and Neural Path Integral -- 3.4.5 Topological Phase Transitions and Hamiltonian Chaos -- 3.4.5.1 Phase Transitions in Hamiltonian Systems -- 3.4.5.2 Geometry of the Largest Lyapunov Exponent -- 3.4.5.3 Euler Characteristics of Hamiltonian Systems -- 4. Quantum Universe -- 4.1 Search for Quantum Gravity -- 4.1.1 What Is Quantum Gravity? -- 4.1.2 Main Approaches to Quantum Gravity -- 4.1.2.1 String Theory -- 4.1.2.2 Loop Quantum Gravity -- 4.1.3 Traditional Approaches to Quantum Gravity -- 4.1.3.1 Discrete Approaches -- 4.1.3.2 Hawking's Euclidean Quantum Gravity -- 4.1.3.3 Effective Perturbative Quantum Gravity -- 4.1.3.4 QFT in Curved Space-Time -- 4.1.3.5 New Approaches to Quantum Gravity -- 4.1.3.6 Hawking's Black Hole Entropy -- 4.2 Loop Quantum Gravity -- 4.2.1 Introduction to Loop Quantum Gravity -- 4.2.2 Formalism of Loop Quantum Gravity -- 4.2.3 Loop Algebra -- 4.2.4 Loop Quantum Gravity -- 4.2.5 Loop States and Spin Network States -- 4.2.6 Diagrammatic Representation of the States -- 4.2.7 Quantum Operators -- 4.2.8 Loop v.s. Connection Representation -- 4.3 Quantum Cosmology -- 4.3.1 Hawking's Cosmology in 'Plain English' -- 4.3.2 Theories of Everything, Anthropic Principle and Wave Function of the Universe -- 4.3.2.1 Quantum Mechanics -- 4.3.2.2 Scientific Reduction -- 4.3.2.3 Anthropic Reasoning in Quantum Cosmology -- 4.3.2.4 Quantum State of the Universe -- 4.3.2.5 From Quantum Mechanics to Quantum Gravity -- 4.3.3 Quantum Gravity and Black Holes -- 4.3.4 Generalized Quantum Mechanics -- 4.3.4.1 Quantum Mechanics Today -- 4.3.4.2 Spacetime and Quantum Theory.

4.3.4.3 The Quantum Mechanics of Closed Systems -- 4.3.4.4 Quantum Theory in 3+1 Form -- 4.3.4.5 Generalized Quantum Theory -- 4.3.4.6 A Quantum Theory of Spacetime Geometry -- 4.3.4.7 Beyond Spacetime -- 4.3.4.8 Emergence/Excess Baggage -- 4.3.4.9 Emergence of Signature -- 4.3.4.10 Beyond Quantum Theory -- 4.3.5 Anthropic String Landscape -- 4.3.5.1 The Landscape -- 4.3.5.2 The Trouble with de Sitter Space -- 4.3.5.3 De Sitter Space is Unstable -- 4.3.5.4 Bubble Cosmology -- 4.3.5.5 Cosmology as a Resonance -- 4.3.6 Top-Down Cosmology -- 4.3.6.1 Trace Anomaly Driven Inflation -- 4.3.6.2 Instability of Anomaly-Induced Inflation -- 4.3.6.3 Origin of Inflation -- 4.3.7 Cosmology in the String Landscape -- 4.3.7.1 Quantum State -- 4.3.7.2 Prediction in Quantum Cosmology -- 4.3.7.3 Anthropic Reasoning -- 4.3.7.4 Models of Inflation -- 4.3.7.5 Prediction in a Potential Landscape -- 4.3.7.6 Alternative Proposals -- 4.3.7.7 Interpretations -- 4.3.8 Brane Cosmology -- 4.3.8.1 The Randall-Sundrum Brane World -- 4.3.8.2 Including a Bulk Scalar Field -- 4.3.8.3 Moving Branes in a Static Bulk -- 4.3.8.4 Cosmology of a Two-Brane System -- 4.3.8.5 Brane Collision -- 4.3.8.6 Open Questions -- 4.3.9 Hawking's Brane New World -- 4.3.9.1 RS Scenario from AdS/CFT -- 4.3.9.2 CFT on the Domain Wall -- 4.3.9.3 The Total Action -- 4.3.9.4 Comparison with 4D Gravity -- 4.3.9.5 Summary on Hawking's Brane New World -- 4.3.10 Brane-World Quantum Cosmology -- 5. Quantum Biophysics in Human Body: Electro-Muscular Stimulation -- 5.1 Basics of Electrical Muscular Stimulation -- 5.2 EMS Functor -- 5.2.1 Global macro-level of EMStotal -- 5.2.2 Local Micro-Level of EMStotal -- 5.2.3 Micro-Level Adaptation and Muscular Training -- 5.3 Electrical Stimulation Fields: EMSfields -- 5.3.1 External Smooth Maxwell Electrodynamics -- 5.3.2 Internal Cellular Bio-Quantum Electrodynamics.

5.4 Stimulated Muscular Contraction Paths: EMSpaths -- 5.4.1 External Anatomical Muscular Mechanics -- 5.4.2 Internal Myofibrillar Bio-Quantum Mechanics -- 5.5 Anatomical Geometry of the Face & Body Shape: EMSgeom -- 5.5.1 External Face & Body Geometry -- 5.5.1.1 Facial Curvatures and Their Deviations -- 5.5.1.2 Facial Riemannian Patch-Manifold -- 5.5.2 Cellular Muscle-Fat Geometry -- 6. Quantum Games and Quantum Computers -- 6.1 Nash's Classical Game Theory -- 6.1.1 Basics of Classical Game Theory -- 6.1.2 Nash Equilibrium: The Focal Point of Game Theory -- 6.1.2.1 Background to Nash Equilibrium -- 6.1.2.2 The Rationalistic Interpretation -- 6.1.2.3 The Mass-Action Interpretation -- 6.2 Quantum Games -- 6.2.1 Quantum Strategies -- 6.2.2 Quantum Games -- 6.2.3 Two-Qubit Quantum Games -- 6.2.3.1 Prisoners' Dilemma -- 6.2.3.2 Chicken Game -- 6.2.4 Quantum Cryptography and Gambling -- 6.3 Formal Quantum Games -- 6.3.1 Formal Framework -- 6.3.2 Various Types of Formal Games -- 6.3.2.1 Strategic Games -- 6.3.2.2 Quantum Simultaneous Games -- 6.3.2.3 Quantum Sequential Games -- 6.3.3 Equivalence of Formal Games -- 6.3.4 Game Classes -- 6.3.5 Summary on Formal Quantum Games -- 6.4 Quantum Information and Computing -- 6.4.1 Entanglement, Teleportation and Information -- 6.4.2 Quantum Computing -- 6.4.2.1 Qubits and Quantum Parallelism -- 6.4.2.2 Quantum Computers -- 6.4.2.3 The Circuit Model for Quantum Computers -- 6.4.2.4 Elementary Quantum Algorithms -- 6.5 The Hardware for Quantum Computers -- 6.5.1 Josephson Effect and Pendulum Analog -- 6.5.1.1 Josephson Effect -- 6.5.1.2 Pendulum Analog -- 6.5.2 Dissipative Josephson Junction -- 6.5.2.1 Junction Hamiltonian and its Eigenstates -- 6.5.2.2 Transition Rate -- 6.5.3 Josephson Junction Ladder (JJL) -- 6.5.3.1 Underdamped JJL -- 6.5.4 Synchronization in Arrays of Josephson Junctions.

6.5.4.1 Phase Model for Underdamped JJL.