Relativistic Quantum Dynamics / Edition 1

by Eugene Stefanovich

Overview

In this third volume of three, quantum electrodynamics is formulated in the language of physical „dressed" particles. A theory where charged particles interact via instantaneous action-at-a-distance forces is constructed - without need for renormalization. This theory describes electromagnetic phenomena in terms of directly interacting charges, but in full accord with fundamental principles of relativity and causality.

Contents
Three ways to look at QFT
Dressing
What are advantages of dressed Hamiltonian?
Coulomb potential and beyond
Decays
RQD in higher orders
Classical electrodynamics
Experimental support of RQD
Particles and relativity
Special theory of relativity
Unitary dressing transformation
Integral for decay law
Coulomb scattering integral in fourth order
Relativistic invariance of Coulomb–Darwin–Breit electrodynamics

Product Details

ISBN-13:	9783110490909
Publisher:	De Gruyter
Publication date:	11/05/2018
Series:	De Gruyter Studies in Mathematical Physics , #47
Pages:	241
Product dimensions:	6.69(w) x 9.45(h) x (d)
Age Range:	18 Years

About the Author

Eugene Stefanovich, Mountain View, CA, USA.

Table of Contents

List of figures xi

List of tables xiii

Postulates, statements, theorems, assertions xv

Conventional notation xvii

Preface xix

1 Three ways to look at QFT 1

1.1 Bare-particle theory 3

1.1.1 Once again about renormalization 4

1.1.2 What is not calculable in QFT? 4

1.1.3 Effective quantum field theory 6

1.2 Clothed-particle theory 7

1.2.1 A bit of history 8

1.2.2 Clothed (physical) particles 8

1.3 Dressed-Hamiltonian theory 9

1.3.1 On origins of QED interaction 10

1.3.2 Earlier attempts at construction of nonfield theories 12

1.3.3 Dressed interactions 13

1.3.4 Comparison with clothed-particle theory 14

1.4 Effective potential in toy model 15

1.4.1 Higher orders of perturbation theory 16

1.4.2 Interactions preserving numbers of particles 17

1.4.3 Interactions changing numbers of particles 18

1.4.4 Energy-momentum spectra 19

2 Dressing 21

2.1 Dressing approach to QED 21

2.1.1 No-self-interaction condition 22

2.1.2 Requirements for dressed interactions 23

2.1.3 Two approaches to dressing 24

2.2 Fitting dressed Hamiltonian to S-operator 24

2.2.1 System of equations 24

2.2.2 Dressed potentials in second order 25

2.2.3 Dressed potentials in third order 27

2.2.4 Dressed potentials in fourth and higher orders 27

2.2.5 What are advantages of dressed Hamiltonian? 28

2.3 Unitary dressing transformation in QED 28

2.3.1 System of equations 29

2.3.2 Unitary dressing in first order 30

2.3.3 Unitary dressing in second order 30

2.3.4 Unitary dressing in higher orders 32

2.3.5 Limit of infinite ultraviolet cutoff 33

2.3.6 Poincaré invariance of dressed theory 34

3 Coulomb potential and beyond 35

3.1 Coulomb-Darwin-Breit Hamiltonian 35

3.1.1 Electron-proton potential in momentum representation 35

3.1.2 Electron-proton potential in position representation 36

3.2 Hydrogen atom 38

3.2.1 Nonrelativistic Schrödinger equation 39

3.2.2 Perturbation theory in hydrogen atom 41

3.2.3 Relativistic energy corrections (orbital) 42

3.2.4 Relativistic energy corrections (spin-orbit) 44

4 Decays 47

4.1 Unstable particle at rest 47

4.1.1 Quantum mechanics of particle decays 47

4.1.2 Noninteracting representation of Poincaré group 50

4.1.3 Normalized eigenvectors of momentum 51

4.1.4 Interacting representation of Poincaré group 52

4.1.5 Decay law 55

4.2 Breit-Wigner formula 56

4.2.1 Schrödinger equation 57

4.2.2 Discrete approximation 61

4.2.3 Mass distribution 64

4.2.4 Exponential decay law 65

4.3 Decay law of moving particle 67

4.3.1 General formula for decay law 67

4.3.2 Decays of states with definite momentum 68

4.3.3 Approximate decay law 70

4.3.4 Decays of states with definite velocity 71

4.4 "Time dilation" in decays 72

4.4.1 Decays in movingframe 72

4.4.2 Numerical results 73

4.4.3 Decays caused by boosts 74

4.4.4 Particle decays in different forms of dynamics 76

5 RQD in higher orders 79

5.1 Spontaneous radiative transitions 79

5.1.1 Bremsstrahlung 80

5.1.2 Bremsstrahlung potential in third order 83

5.1.3 Instability of excited atomic states 85

5.1.4 Rate of radiative transition 86

5.2 Radiative corrections to interaction potential 88

5.2.1 Product of potentials in (5.2) 88

5.2.2 Radiative corrections to Coulomb potential 90

5.3 Electron anomalous magnetic moment 91

5.3.1 Electron magnetic moment in second order 91

5.3.2 Fourth-order correction 92

5.4 Lamb shift 92

5.4.1 Experimental data 92

5.4.2 Contribution from potential V₃^d 93

5.4.3 Contribution from potential V₃^d 96

6 Classical electrodynamics 99

6.1 Maxwell's theory in a nutshell 99

6.1.1 Structure of fields and interactions 99

6.1.2 Conservation laws 100

6.1.3 Energy and momentum of electromagnetic field 101

6.2 Interaction of classical charges in RQD 102

6.2.1 Coulomb-Darwin-Breit Hamiltonian 102

6.2.2 Two charges 104

6.2.3 Definition of force 106

6.2.4 Conservation laws in RQD 107

6.2.5 Trouton-Noble paradox 107

6.2.6 Electromagnetic field or photons? 109

6.3 Magnetic interactions 109

6.3.1 Charge + straight wire with current 109

6.3.2 Longitudinal forces in wires 112

6.3.3 Charge + wire loop 113

6.3.4 Charge + spin's magnetic moment 116

6.3.5 Two types of magnets 117

6.3.6 Thin long magnet/solenoid 118

6.3.7 Cylindrical magnet/solenoid of arbitrary cross section 119

6.3.8 Cullwick paradox 120

7 Experimental support of RQD 125

7.1 Electromagnetic induction 125

7.1.1 Moving magnets 125

7.1.2 Homopolar generator 127

7.2 Aharonov-Bohm effect 129

7.2.1 Aharonov-Bohm effect with linear magnet 129

7.2.2 Aharonov-Bohm effect with toroidal magnet 131

7.3 Experimental studies of bound fields 133

7.3.1 Three types of force fields 133

7.3.2 Force fields emitted by antennas 135

7.3.3 Studies in the near field 136

7.3.4 Microwave horn antennas 136

7.4 Relativistic electron bunches 137

7.4.1 Fast moving charge (RQD) 138

7.4.2 Fast moving charge (Maxwell's theory) 141

7.4.3 Charge leaving accelerator (Maxwell's theory) 142

7.4.4 Charge leaving accelerator (RQD) 143

7.4.5 Frascati experiment 144

8 Particles and relativity 147

8.1 Localizability of particles 148

8.1.1 Measurements of position 149

8.1.2 Localized states in moving frame 149

8.1.3 Spreading of localized states 150

8.1.4 Superluminal spreading and causality 151

8.1.5 Transformations of quantum fields 153

8.2 Inertial transformations without interaction 154

8.2.1 Events and observables 154

8.2.2 Two noninteracting particles 155

8.2.3 Boosts of trajectories 156

8.2.4 Lorentz transformations 157

8.3 Inertial transformations with interaction 159

8.3.1 Time translations 159

8.3.2 Boosts 160

8.3.3 Rotations 162

8.3.4 Space translations 162

8.3.5 Support of instant form dynamics 163

8.3.6 Physical inequivalence of forms of dynamics 164

8.3.7 Currie-Jordan-Sudarshan theorem 165

8.4 Do instantaneous interactions violate causality? 169

8.4.1 Interaction in different frames of reference 169

8.4.2 Frascati experiment in moving reference frame 171

8.4.3 Does Frascati experiment violate causality? 172

8.5 Comparison with special relativity 173

8.5.1 Are Lorentz transformations universal? 173

8.5.2 About "derivations" of Lorentz transformations 174

8.5.3 Poincaré invariance vs. manifest covariance 175

8.5.4 About time measurements 176

8.5.5 Is world's geometry four-dimensional? 176

8.5.6 Experimental checks of special relativity 177

8.6 Why do we need quantum fields? 178

8.6.1 Are quantum fields measurable? 179

8.6.2 Quantum fields and space-time 179

8.6.3 Renormalization and dressing in a nutshell 181

8.6.4 What is next? 183

9 Summary 185

A Special theory of relativity 187

A.1 Lorentz transformations for time and position 187

A.2 Manifest covariance 188

A.3 Decay of moving particle in special relativity 188

A.4 Ban on superluminal signals 189

B Unitary dressing transformation 191

C Integral for decay law 193

D Coulomb scattering integral in fourth order 197

E Relativistic invariance of Coulomb-Darwin-Breit electrodynamics 201

Bibliography 205

Index 217