Light And Vacuum: The Wave-Particle Nature Of The Light And The Quantum Vacuum Through The Coupling Of Electromagnetic Theory And Quantum Electrodynamics

Light And Vacuum: The Wave-Particle Nature Of The Light And The Quantum Vacuum Through The Coupling Of Electromagnetic Theory And Quantum Electrodynamics

by Meis Constantin


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Product Details

ISBN-13: 9789814630894
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 11/10/2014
Pages: 136
Product dimensions: 6.00(w) x 9.10(h) x 0.60(d)

Table of Contents

Prologue ix

1 Introduction 1

2 Historical Survey and Experimental Evidence 3

The concepts of light during the last 2500 years: corpuscles, ray optics, wave optics, electromagnetic wave theory and finally quantum, particle theory 3

Bibliography 8

3 Basic Principles of the Electromagnetic Wave Theory 11

3.1 Maxwell's Equations 11

3.2 Electromagnetic Wave Propagation 14

Dispersion relation 14

Physical quantities involved in the electromagnetic field 16

Propagation equations of electromagnetic waves 18

Helmholtz equation 18

Energy flux of electromagnetic waves 19

TEM waves - Laplace equation 21

3.3 Scalar and Vector Potentials 23

3.4 Vector Potential and Electromagnetic Field Polarization 25

3.5 Guided Propagation of Electromagnetic Waves 28

Rectangular waveguide of cross section a, b(a>b) 29

3.5.1 TEm,n Modes 29

3.5.2 TMm,n Components 30

Circular waveguide of radius r0 31

3.5.3 TEm,n Modes 31

3.5.4 TMm,n Modes 32

Case of two parallel plates 33

Density of states 34

3.6 Conclusion Remarks 35

Bibliography 36

4 From Electromagnetic Waves to Quantum Electrodynamics 39

4.1 Elements of Quantum Mechanics 39

Blackbody radiation and the ultraviolet catastrophe 39

Energy and momentum operators in quantum mechanics 41

Particle in a square potential well - correspondence with the waveguides 43

4.2 Harmonic Oscillator in Quantum Mechanics 44

From the classical expressions to the quantum mechanical ones 44

Dirac representation, creation and annihilation operators a, a+ 47

4.3 Quantum Electrodynamics (QED) and the Photon Description 49

Brief description of selected experiments that have historically played an important role for the introduction of the photon concept 49

The photoelectric effect and the quantum interpretation 49

Compton scattering 50

Low intensity Young's double-slit interferences 51

4.3.1 Second Quantization 52

Quantization process of the electromagnetic field 52

4.4 Interaction between Electromagnetic Waves and Charged Particles, Reality of the Vector Potential 56

Interaction Hamiltonian between an electromagnetic wave and a charged particle 56

Reality of the vector potential, Ehrenberg Siday or Aharonov-Bohm effect 57

4.5 Transition Rates and Vacuum Induced Spontaneous Emission 57

Photoelectric effect and the semi-classical interpretation 60

Spontaneous emission rate 61

Dipole approximation and the spontaneous emission 62

The photon spin 63

4.6 Lamb Shift 63

Nonrelativistic calculations: Bethe's approach 63

4.7 Conclusion Remarks 67

Bibliography 68

5 Theory. Experiments and Questions 71

5.1 Planck's Constant and the Vacuum Intrinsic Electromagnetic Properties 71

5.2 Hamiltonian Issued from the Quantization of the Electromagnetic Field 73

5.3 QED Singularities 74

5.4 Electron-Vacuum Interactions and the Associated Effects 75

Spontaneous emission 76

Lamb shift 77

Casimir effect 79

5.5 Simultaneous Wave-particle Nature of the Photon Revealed by the Experiments - Discussions 80

Photoelectric effect and Young's double-slit experiment SO

Mizobuchi and Ohtake double-prism experiment 81

Grangier's et al. experiments, photon indivisibility 83

Hunter Wadlinger experiments, the photon spatial expansion 83

5.6 Conclusion Remarks 85

Bibliography 86

6 Analysis of the Electromagnetic Field Quantization Process and the Photon Vector Potential. The Non- Local Photon Wave-Particle Representation and the Quantum Vacuum 89

6.1 Quantized Vector Potential Amplitude of a Single Photon State 89

Dimension analysis from Maxwell's equations. Vector potential amplitude proportional to the frequency 89

Wave equation for the photon vector potential 91

Photon wavelength dimensions following the experimental evidence 93

Wave-particle formalism 95

Relation between the photon vector potential and the electron charge 97

6.2 Quantum Vacuum Representation 98

6.3 The Quantum Vacuum Field Effects 102

Spontaneous emission 102

Lamb shift 104

Cosmic vacuum energy density 106

6.4 Conclusion Remarks 107

Bibliography 108

7 Epilogue 111

Index 115

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