Modified Maxwell equations in quantum electrodynamics

Divergencies in quantum field theory referred to as "infinite zero-point energy" have been a problem for 70 years. Renormalization has always been considered an unsatisfactory remedy. In 1985 it was found that Maxwell's equations generally do not have solutions that satisfy the causality law. An additional term for magnetic dipole currents corrected this shortcoming. Rotating magnetic dipoles produce magnetic dipole currents, just as rotating electric dipoles in a material like barium titanate produce electric dipole currents. Electric dipole currents were always part of Maxwell's equations. This book shows that the correction of Maxwell's equations eliminates the infinite zero-point energy in quantum electrodynamics. In addition, it presents many more new results. Machine generated contents note: PREFACE VII LIST OF FREQUENTLY USED SYMBOLS XI 1 Introduction 1.1 Maxwell's Equations 1 1.2 Step Function Excitation of Planar TEM Wave 6 1.3 Solutions for the Electric Field Strength 9 1.4 Associated Magnetic Field Strength 13 1.5 Field Strengths with Continuous Time Variation 20 1.6 Modified Maxwell Equations in Potential Form 22 2 Monopole, Dipole, and Multipole Currents 2.1 Electric Monopoles and Dipoles With Constant Mass 27 2.2 Magnetic Monopoles and Dipoles With Constant Mass 37 2.3 Monopoles and Dipoles With Relativistic Variable Mass 44 2.4 Covariance of the Modified Maxwell Equations 53 2.5 Energy and Momentum With Dipole Current Correction 61 3 Hamiltonian Formalism 3.1 Undefined Potentials and Divergent Integrals 68 3.2 Charged Particle in an Electromagnetic Field 78 3.3 Variability of the Mass of a Charged Particle 88 3.4 Steady State Solutions of the Modified Maxwell Equations 98 3.5 Steady State Quantization of the Modified Radiation Field 108 4 Quantization of the Pure Radiation Field 4.1 Radiation Field in Extended Lorentz Gauge 113 4.2 Simplification of Aev((,0) and Amv((, 9) 135 4.3 Hamilton Function for Planar Wave 140 4.4 Quantization of a Planar Wave 147 4.5 Exponential Ramp Function Excitation 150 4.6 Excitation With Rectangular Pulse 158 5 Klein-Gordon Equation and Vacuum Constants 5.1 Modified Klein-Gordon Equation 160 5.2 Planar Wave Solution 168 5.3 Hamilton Function for the Planar Klein-Gordon Wave 179 5.4 Quantization of the Planar Klein-Gordon Wave 184 5.5 Dipole Current Conductivities in Vacuum 187 6 Appendix 6.1 Electric Field Strength Due to Electric Step Function 192 6.2 Magnetic Field Strength Due to Electric Step Function 199 6.3 Excitation by a Magnetic Step Function 210 6.4 Electric Field Strength Due to Electric Ramp Function 216 6.5 Magnetic Field Strength Due to Electric Ramp Function 220 6.6 Component Amz of the Vector Potential 224 6.7 Component Ae of the Vector potential 231 6.8 Choice of p2 1 in Eq.(4.1-85) 238 6.9 Excitation of a Spherical Wave 240 6.10 Better Approximations of Dipole Currents 245 6.11 Evaluation of Eq.(5.3-4) 259 6.12 Calculations for Sections 4.2 and 4.3 271 REFERENCES AND BIBLIOGRAPHY 291 INDEX 297. 1. Introduction. 1.1. Maxwell's equations. 1.2. Step function excitation of planar TEM wave. 1.3. Solutions for the electric field strength. 1.4. Associated magnetic field strength. 1.5. Field strengths with continuous time variation. 1.6. Modified Maxwell equations in potential form -- 2. Monopole, dipole, and multipole currents. 2.1. Electric monopoles and dipoles with constant mass. 2.2. Magnetic monopoles and dipoles with constant mass. 2.3. Monopoles and dipoles with relativistic variable mass. 2.4. Covariance of the modified Maxwell equations. 2.5. Energy and momentum with dipole current correction -- 3. Hamiltonian formalism. 3.1. Undefined potentials and divergent integrals. 3.2. Charged particle in an electromagnetic field. 3.3. Variability of the mass of a charged particle. 3.4. Steady state solutions of the modified Maxwell equations. 3.5. Steady state quantization of the modified radiation field -- 4. Quantization of the pure radiation field. 4.1. Radiation field in extended Lorentz gauge. 4.2. Simplification of Aev([symbol]) and Amv([symbol]). 4.3. Hamilton function for planar wave. 4.4. Quantization of a planar wave. 4.5. Exponential ramp function excitation. 4.6. Excitation with rectangular pulse -- 5. Klein-Gordon equation and vacuum constants. 5.1. Modified Klein-Gordon equation. 5.2. Planar wave solution. 5.3. Hamilton function for the planar Klein-Gordon wave. 5.4. Quantization of the planar Klein-Gordon wave. 5.5. Dipole current conductivities in vacuum