Quantum leap: From Dirac and Feynman, across the Universe, to human body and mind

Description

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 cosm.  Read more... Abstract: 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 cosm Content: Preface Acknowledgments Contents 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 Electrodynamics2.2.1 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. 3.1.4 Statistical Mechanics via Path Integrals3.1.5 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 Interpretation3.2.4 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.