QUANTUM OPTICS
CONTENTS PART I: BASIC CONCEPTS AND PRINCIPLES OUTLINE OF THE BOOK PART I: BASIC CONCEPTS AND PRINCIPLES PART II: THE MEANING OF QUANTUM MECHANICS PART III: THE SYMMETRIES OF SPACE AND TIME PART IV: CONSERVATIVE CLASSICAL MECHANICS PART V: THE DYNAMICS OF QUANTUM SYSTEMS PART VI: REPRESENTATIONS OF GROUPS AND LIE ALGEBRAS CONTINUOUS AND INFINITESIMAL SYMMETRIES SYMMETRIES A BIT OF HISTORY WHAT IS A SYMMETRY? MATRICES BASICS ON LIE ALGEBRAS LIE ALGEBRAS ISOMORPHISMS AND COMMUTATION RELATIONS MATRIX LIE ALGEBRAS FURTHER CONCEPTS FOR LIE ALGEBRAS SOME CONSTRUCTIONS UNIVERSAL ENVELOPING ALGEBRA AND CASIMIRS GROUPS GROUP HOMOMORPHISMS AND SEMIDIRECT PRODUCTS GROUP REPRESENTATIONS FURTHER CONCEPTS FOR GROUPS MATRIX GROUPS AND CONTINUOUS MOTIONS MATRIX GROUPS MOTIONS INFINITESIMAL MOTIONS THE IDENTITY SUBGROUP UNIFORM MOTIONS AND THE MATRIX EXPONENTIAL THE UNIVERSAL COVERING GROUP DISCRETE GROUPS CLASSICAL MECHANICS AND QUANTUM MECHANICS A HIERARCHICAL VIEW OF PHYSICS UNITS LENGTH SCALES THE BASIC LIMITS OF PHYSICS THE MAIN HIERARCHY OF FIELDS OF PHYSICS CLASSICAL MECHANICS PARTICLE MECHANICS CONTINUUM MECHANICS RELATIVITY THEORY STATISTICAL MECHANICS AND THERMODYNAMICS HAMILTONIAN MECHANICS QUANTUM MECHANICS THE CORRESPONDENCE PRINCIPLE THE SCHRÖDINGER PICTURE BRAS AND KETS THE HEISENBERG PICTURE INTERACTION PICTURES THE CANONICAL ENSEMBLE QUANTUM FIELD THEORY DETERMINISTIC AND STATISTICAL PREDICTIONS MEASUREMENT IN QUANTUM MECHANICS THE QUANTUM MEASUREMENT PROCESS QUANTUM SOURCES AND STATES MEASUREMENT DEVICES AND QUANTUM MEASURES THE STATISTICAL INTERPRETATION STATISTICAL EXPECTATIONS THE STATISTICAL INTERPRETATION OF QUANTUM MECHANICS THE SPECTRAL VERSION OF BORN’S RULE QUANTUM TOMOGRAPHY QUANTUM MEASUREMENT TOMOGRAPHY AND POVMS INFORMATIONALLY COMPLETE QUANTUM MEASURES QUANTUM STATE TOMOGRAPHY COMPLETELY POSITIVE MAPS AND QUANTUM PROCESS TOMOGRAPHY NONSTATIONARY SOURCES QUANTUM TOMOGRAPHY OF INSTRUMENTS COMPOSITE SOURCES, FILTERS, AND DETECTORS QUANTUM DYNAMICS AND SPECTROSCOPY QUANTUM DYNAMICS QUANTUM BEAMS AND QUANTUM LIOUVILLE EQUATION QUANTUM PHASE SPACE THE EHRENFEST PICTURE PURE STATE IDEALIZATION AND THE SCHRÖDINGER EQUATION QUANTUM DYNAMICS IN MIXING LINEAR MEDIA NONLINEAR DISSIPATIVE QUANTUM DYNAMICS SPECTROSCOPY AND SYSTEM IDENTIFICATION ENERGY SPECTRUM AND QUANTUM FLUCTUATIONS SPECTROSCOPY AND HIGH PRECISION MEASUREMENTS EXAMPLE: THE GYROMAGNETIC RATIO OF THE ELECTRON QUANTUM FIELDS AND MACROSCOPIC QUANTUM SYSTEMS EXTENDED SOURCES THE EMERGENCE OF QUANTUM FIELDS MACROSCOPIC QUANTUM SYSTEMS ON THE FOUNDATIONS OF QUANTUM MECHANICS MEASUREMENT UNCERTAINTY STATISTICAL UNCERTAINTY IMPERFECT MEASUREMENTS MEASUREMENT ERRORS QUANTUM MEASURES FOR PARTICULAR DETECTORS BEAM SPLITTERS AND POLARIZATION STATE MEASUREMENTS JOINT MEASUREMENTS OF NONCOMMUTING QUANTITIES REALISTIC MEASUREMENTS OF POSITION MEASURING PARTICLE TRACKS ON THE INTERPRETATION OF QUANTUM MECHANICS THE ORIGIN OF DISCRETE RANDOMNESS THE QUANTUM MEASUREMENT PROBLEM PARTICLES AND FIELDS THE UNIVERSE AS A QUANTUM SYSTEM REPRODUCIBILITY AND OBJECTIVITY KNOWLEDGE AND PROBABILITY THE THERMAL INTERPRETATION OF QUANTUM PHYSICS ROTATIONS AND TRANSLATIONS ROTATIONS AND SO(N) 3-VECTORS 3-DIMENSIONAL ROTATIONS AND SO(3) THE EXPONENTIAL MAP PAULI MATRICES AND QUATERNIONS PAULI MATRICES PAULI 4-VECTORS QUATERNIONS AND ROTATIONS RIGID MOTION AND ANGULAR MOMENTUM RIGID MOTIONS AND EUCLIDEAN GROUPS ROTATING RIGID BODIES ROTATIONS AND ANGULAR MOMENTUM CLASSICAL RIGID BODY DYNAMICS UNITARY GROUPS: FEW-LEVEL SYSTEMS, QUBITS, QUARKS N-LEVEL SYSTEMS AND U(N) ATOMIC ENERGY LEVELS N-LEVEL SYSTEMS ROTATIONS AND SU(2) THE ISOMORPHISM SU(2) ?SO(3) QUBITS AND BLOCH SPHERE POLARIZED LIGHT AND BEAM TRANSFORMATIONS HISTORICAL REMARKS LIGHT AND MAXWELL EQUATIONS THE STERN–GERLACH EXPERIMENT THE QUARK MODEL AND SU(3) LIE GROUPS AND LIE ALGEBRAS MOTIONS ON VECTOR SPACES AND LIE ALGEBRAS MOTIONS ON VECTOR SPACES LIE PRODUCTS AND LIE COPRODUCTS SOME LIE ALGEBRA CONSTRUCTIONS ADJOINT AND COADJOINT REPRESENTATION LINEAR GROUPS AND THEIR LIE ALGEBRAS TIME-ORDERED EXPONENTIAL AND UNIFORM MOTIONS THE LIE ALGEBRA OF INFINITESIMAL MOTIONS MOTIONS IN INFINITE DIMENSIONS LIE ALGEBRAS FROM DERIVATIONS LIE ?-ALGEBRAS COMPLEXIFICATION LINEAR LIE GROUPS IMPORTANT FAMILIES OF LIE ALGEBRAS CLASSICAL LIE GROUPS AND THEIR LIE ALGEBRAS THE GENERAL LINEAR GROUP GL(N, ??) THE SPECIAL LINEAR GROUP SL(N, ??) GROUPS AND LIE ALGEBRAS PRESERVING BILINEAR FORMS THE ORTHOGONAL GROUPS O(N, ??) AND O(P, Q) THE GROUPS SO(P, Q) AND ISO(P, Q) THE SYMPLECTIC GROUP SP(2N, ??) THE UNITARY GROUPS U(N) AND SU(N) FINITE-DIMENSIONAL SEMISIMPLE LIE ALGEBRAS COMPOSITE LIE ALGEBRAS AND LIE GROUPS HEISENBERG ALGEBRAS HEISENBERG GROUPS THE HEISENBERG EXTENSION OF A LIE ALGEBRA SYMMETRIES OF SPACETIME MINKOWSKI SPACETIME MINKOWSKI SPACE CAUSALITY GENERAL SPACETIME THE POINCARÉ GROUP LOCAL LORENTZ TRANSFORMATIONS THE FAMILY OF LORENTZ GROUPS LORENTZ TRANSFORMATIONS OF SPECIAL FORM ORBITS OF THE PROPER LORENTZ GROUP INFINITESIMAL LORENTZ TRANSFORMATIONS THE 4-DIMENSIONAL CASE SL(2, ?) AS DOUBLED LORENTZ GROUP COVERING THE DISCRETE SYMMETRIES P AND T THE LORENTZ LIE ALGEBRA SO(1, 3) THE POINCARÉ GROUP ISO(1, 3) THE DOUBLED POINCARÉ GROUP THE NONRELATIVISTIC LIMIT GALILEAN SPACETIME AND THE GALILEAN GROUP CLASSICAL OSCILLATING SYSTEMS SYSTEMS OF DAMPED OSCILLATORS MULTIMODAL POTENTIALS PHASE SPACE FORMULATION THE CLASSICAL ANHARMONIC OSCILLATOR THE ANHARMONIC OSCILLATOR IN PHASE SPACE THE CLASSICAL HARMONIC OSCILLATOR HARMONIC OSCILLATORS AND LINEAR FIELD EQUATIONS ALPHA RAYS BETA RAYS LIGHT RAYS AND GAMMA RAYS CONSERVATIVE CLASSICAL MECHANICS POISSON ALGEBRAS FOR CLASSICAL MECHANICS POISSON ALGEBRAS LIE–POISSON ALGEBRAS POISSON REPRESENTATIONS OF SYMPLECTIC LIE ALGEBRAS CLASSICAL SYMPLECTIC MECHANICS COMMUTATIVE POISSON ALGEBRAS FROM CLOSED 2-FORMS THE SYMPLECTIC CASE CLASSICAL CONSERVATIVE HAMILTONIAN DYNAMICS UNCONSTRAINED HAMILTONIAN DYNAMICS CONSTRAINED HAMILTONIAN DYNAMICS A HAMILTONIAN SYSTEM WITH GAUGE SYMMETRY A VARIATIONAL PRINCIPLE CLASSICAL LAGRANGIAN MECHANICS MOLECULAR MECHANICS HAMILTONIAN QUANTUM MECHANICS HERMITIAN SPACES HERMITIAN SPACES AND THEIR ANTIDUAL NORM AND COMPLETION OF A HERMITIAN SPACE LINEAR MAPPINGS BETWEEN HERMITIAN SPACES QUANTUM DYNAMICS AS SYMPLECTIC MOTION THE DIRAC–FRENKEL VARIATIONAL PRINCIPLE QUANTUM-CLASSICAL DYNAMICS EXAMPLES QUANTUM-CLASSICAL DYNAMICS IN THE HEISENBERG PICTURE QUANTIZATION BEREZIN QUANTIZATION AND GEOMETRIC QUANTIZATION DEFORMATION QUANTIZATION THE WIGNER TRANSFORM THE SYMBOL FORMULATION QUANTUM OSCILLATORS AND COHERENT STATES QUANTIZING THE HARMONIC OSCILLATOR EXTENSION TO THE ANHARMONIC CASE THE OSCILLATOR ALGEBRA OS(1) REPRESENTATIONS OF THE HEISENBERG ALGEBRA THE SINGLE-MODE BOSON FOCK SPACE COHERENT STATES FOR THE HARMONIC OSCILLATOR GROUP COHERENT STATES GLAUBER COHERENT STATES RESOLUTION OF UNITY THE BARGMANN REPRESENTATION MONOCHROMATIC BEAMS AND COHERENT STATES DYNAMICAL EQUATIONS FOR QUANTUM SYSTEMS HAMILTONIANS HAMILTONIANS IN AN N-LEVEL SYSTEM THE QUANTUM SPECTRUM THE SPECTRAL THEOREM: INFORMAL VERSION THE SPECTRAL THEOREM: USES THE SPECTRAL THEOREM: SEMIFORMAL VERSION THE SPECTRAL THEOREM: RIGOROUS VERSION SOLVING THE HEISENBERG, LIOUVILLE, AND SCHRÖDINGER EQUATION DYNAMICS IN THE HEISENBERG PICTURE THE QUANTUM LIOUVILLE EQUATION DYNAMICS IN THE SCHRÖDINGER PICTURE REPRESENTATION THEORY REPRESENTATIONS OF MATRIX LIE GROUPS LINEAR REPRESENTATIONS PROJECTIVE REPRESENTATIONS REPRESENTATIONS OF LIE ALGEBRAS GENERAL REPRESENTATIONS TRIANGULAR DECOMPOSITIONS THE SEMISIMPLE CASE TRIANGULATED LIE ALGEBRAS OF RANK AND DEGREE ONE CLASSIFICATION FOR RANK AND DEGREE ONE UNITARY HIGHEST WEIGHT REPRESENTATIONS REPRESENTATIONS FOR QUANTUM PARTICLES LINEAR REPRESENTATIONS OF GL(2, ?) AND SU(2) SPIN PAULI SETS TRIDIAGONAL FORM THE SPINOR REPRESENTATIONS OF GL(2, ?) SPIN COHERENT STATES THE COMPLETENESS RELATION ELEMENTARY PARTICLES MASS AND SPIN CASIMIRS PHYSICAL REPRESENTATIONS OF THE POINCARÉ GROUP THE SPINOR REPRESENTATIONS DEFINITENESS LORENTZ INVARIANT MEASURES SPECTRA AND SPECTROSCOPY PROBING THE SPECTRUM OF A SYSTEM FROM THE EARLY HISTORY OF QUANTUM MECHANICS SPECTRAL LINES THE HYDROGEN SPECTRUM NOBEL PRIZES FOR THE PIONEERS OF QUANTUM MECHANICS BLACK BODY RADIATION EINSTEIN’S DERIVATION OF PLANCK’S LAW MODERN DERIVATION OF PLANCK’S LAW STEFAN’S LAW AND WIEN’S DISPLACEMENT LAW SPECTRA OF SYSTEMS OF PARTICLES EXAMPLES OF SPECTRA SPECTRUM DEFORMATION AND AVOIDED CROSSINGS DYNAMICAL SYMMETRIES SYMMETRIES AND BROKEN SYMMETRIES CHAINS OF SUBALGEBRAS BRANCHING RULES CLEBSCH–GORDAN COEFFICIENTS THE HYDROGEN ATOM SYMMETRIES OF THE HYDROGEN ATOM SYMMETRY BREAKING IN THE HYDROGEN ATOM KEPLER’S LAWS, THE HYDROGEN ATOM, AND SO(4)