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Ivancevic V.G., Ivancevic T.T. Quantum Leap: From Dirac and Feynman, Across the Universe, to Human Body and Mind

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Ivancevic V.G., Ivancevic T.T. Quantum Leap: From Dirac and Feynman, Across the Universe, to Human Body and Mind
Singapore: World Scientific Publishing Company, 2008. — 855 p.
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body all from the perspective of quantum mechanics and quantum field theory. This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness. It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia. Contents: Elements of Quantum Mechanics; Feynman Path Integrals; Quantum Universe; Quantum Biophysics in Human Body: Electro Muscular Stimulation; Quantum Games and Quantum Computers; Quantum Mind.
Preface
Acknowledgments
Soft Introduction to Quantum Mechanics
Quantum Hilbert Space
Formal Hilbert Space
Human Intelligence, Mind and Reason
Human Reason
Basics of Non–Relativistic Quantum Mechanics
Canonical Quantization
Quantum States and Operators
Quantum Pictures
Spectrum of a Quantum Operator
General Representation Model
Direct Product Space
State–Space for n Quantum Particles
Difficulties of the Relativistic Quantum Mechanics
Particles of Half–Odd Integral Spin
Particles of Integral Spin
Dirac’s Electrodynamics Action Principle
Dirac Equation and Formal QED in Brief
Lorentzian Space-Time and Gravity
Unification of Fundamental Interactions
First Unification
Path Integrals: Sums Over Histories
Classical Probability Concept
Quantum Probability Concept
Quantum Coherent States
Dirac’s hbra | keti Transition Amplitude
Feynman’s Sum–over–Histories
The Basic Form of a Path Integral
Adaptive Path Integral
Extract from Feynman’s Nobel Lecture
Lagrangian Path Integral
Hamiltonian Path Integral
Feynman–Kac Formula
Canonical versus Path–Integral Quantization
Sources
Fields
Gauges
Riemannian–Symplectic Geometries
Statistical Mechanics via Path Integrals
Path–Integral Monte–Carlo Simulation
Sum over Geometries and Topologies
Simplicial Quantum Geometry
Discrete Gravitational Path Integrals
Regge Calculus
Lorentzian Path Integral
Path Integrals and Green’s Functions
Topological Quantum Field Theory
TQFT and Seiberg–Witten Theory
SW Invariants and Monopole Equations
Topological Lagrangian
Quantum Field Theory
Dimensional Reduction and D Field Theory
Geometrical Interpretation
TQFTs Associated with SW–Monopoles
Dimensional Reduction
TQFTs of D Monopoles
Non–Abelian Case
Strings
Interactions
Loop Topology of Closed Surfaces
Transition Amplitudes for Strings
Weyl Invariance and Vertex Operator Formulation
Transition Amplitude for a Single Point Particle
Witten’s Open String Field Theory
Operator Formulation of String Field Theory
Open Strings
Construction of Overlap Vertices
Transformation of String Fields
Topological Strings
Geometrical Transitions
Topological Strings and Black Hole Attractors
Stochastic Optimal Control
Path–Integral Formalism
Monte Carlo Sampling
Nonlinear Dynamics of Option Pricing
Theory and Simulations of Option Pricing
Option Pricing via Path Integrals
Continuum Limit and American Options
Continuum Limit of the Kuramoto Net
Path–Integral for Complex Networks
Cerebellum as a Neural Path–Integral
Spinal Autogenetic Reflex Control
Cerebellum – the Comparator
Hamiltonian Action and Neural Path Integral
Phase Transitions in Hamiltonian Systems
Geometry of the Largest Lyapunov Exponent
Euler Characteristics of Hamiltonian Systems
What Is Quantum Gravity?
String Theory
Loop Quantum Gravity
Discrete Approaches
Hawking’s Euclidean Quantum Gravity
QFT in Curved Space–Time
New Approaches to Quantum Gravity
Hawking’s Black Hole Entropy
Introduction to Loop Quantum Gravity
Formalism of Loop Quantum Gravity
Loop Algebra
Loop Quantum Gravity
Loop States and Spin Network States
Diagrammatic Representation of the States
Quantum Operators
Loop vs Connection Representation
Quantum Cosmology
Hawking’s Cosmology in ‘Plain English’
Theories of Everything, Anthropic Principle and Wave Function of the Universe
Quantum Mechanics
Scientific Reduction
Anthropic Reasoning in Quantum Cosmology
Quantum State of the Universe
From Quantum Mechanics to Quantum Gravity
Quantum Gravity and Black Holes
Generalized Quantum Mechanics
Quantum Mechanics Today
Spacetime and Quantum Theory
The Quantum Mechanics of Closed Systems
Quantum Theory in + Form
Generalized Quantum Theory
A Quantum Theory of Spacetime Geometry
Beyond Spacetime
Emergence/Excess Baggage
Emergence of Signature
Beyond Quantum Theory
Anthropic String Landscape
The Landscape
The Trouble with de Sitter Space
De Sitter Space is Unstable
Bubble Cosmology
Cosmology as a Resonance
Top–Down Cosmology
Trace Anomaly Driven Inflation
Instability of Anomaly–Induced Inflation
Origin of Inflation
Cosmology in the String Landscape
Quantum State
Prediction in Quantum Cosmology
Anthropic Reasoning
Models of Inflation
Prediction in a Potential Landscape
Alternative Proposals
Interpretations
Brane Cosmology
The Randall–Sundrum Brane World
Including a Bulk Scalar Field
Moving Branes in a Static Bulk
Cosmology of a Two–Brane System
Brane Collision
Open Questions
Hawking’s Brane New World
RS Scenario from AdS/CFT
CFT on the Domain Wall
The Total Action
Comparison with D Gravity
Summary on Hawking’s Brane New World
Brane–World Quantum Cosmology
Basics of Electrical Muscular Stimulation
EMS Functor
Global macro–level of EMStotal
Local Micro–Level of EMStotal
Micro–Level Adaptation and Muscular Training
External Smooth Maxwell Electrodynamics
Internal Cellular Bio–Quantum Electrodynamics
External Anatomical Muscular Mechanics
Internal Myofibrillar Bio–Quantum Mechanics
Facial Curvatures and Their Deviations
Facial Riemannian Patch–Manifold
Cellular Muscle–Fat Geometry
Nash’s Classical Game Theory
Basics of Classical Game Theory
Background to Nash Equilibrium
The Rationalistic Interpretation
The Mass–Action Interpretation
Quantum Games
Quantum Strategies
Quantum Games
Two–Qubit Quantum Games
Prisoners’ Dilemma
Chicken Game
Quantum Cryptography and Gambling
Formal Quantum Games
Formal Framework
Various Types of Formal Games
Quantum Simultaneous Games
Quantum Sequential Games
Equivalence of Formal Games
Summary on Formal Quantum Games
Entanglement, Teleportation and Information
Quantum Computing
Quantum Computers
The Circuit Model for Quantum Computers
Elementary Quantum Algorithms
The Hardware for Quantum Computers
Josephson Effect
Pendulum Analog
Dissipative Josephson Junction
Junction Hamiltonian and its Eigenstates
Transition Rate
Josephson Junction Ladder (JJL)
Underdamped JJL
Synchronization in Arrays of Josephson Junctions
Phase Model for Underdamped JJL
Comparison of LKM and RCSJ Models
‘Small–World’ Connections in JJL Arrays
Human Mind
The Mind–Body Problem
EPR Paradox
Bell’s Theorem
Orchestrated Reduction and Penrose Paradox
Orchestrated Objective Reduction
The Orch OR Model
Physical Science and Consciousness
Reducing the Consciousness to Its Elements
Manipulation of Consciousness
A Need for Paradigm–Shift
Quantum Synapses
Biochemistry of Microtubules
Kink Soliton Model of MT–Dynamics
Liouville–Hamiltonian Neurodynamics
Dissipative Quantum Brain Model
QED Brain
Theory of Mind and Matter
Matter
Mind
Unification
Quantum Consciousness
The Experiment
Bio–Active Peptides
Drugs
Quantum–Like Psychodynamics
Life Space Foam
Joint Action Psychodynamics
Feynman–Finsler Approach to Adaptation
Bibliography
Index
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