New Aspects of Quantum Electrodynamics

197 Pages·2017·7.479 MB·English

by  Akitomo Tachibana (auth.)

Akitomo Tachibana
New Aspects
of Quantum
Electrodynamics
New Aspects of Quantum Electrodynamics
Akitomo Tachibana
New Aspects of Quantum
Electrodynamics
AkitomoTachibana
DepartmentofMicroEngineering
KyotoUniversity
Kyoto,Japan
ISBN978-981-10-3131-1 ISBN978-981-10-3132-8 (eBook)
DOI10.1007/978-981-10-3132-8
LibraryofCongressControlNumber:2016960671
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Preface
Quantum Mechanics: 100 Years of Mystery Solved!
In the theoretical study of the application of quantum electrodynamics (QED),
recent progress in research has led to solving the mystery (as Feynman said)
involved in the foundation of quantum mechanics. Because this is a very big
achievement, we will first note this breakthrough in the title of this preface, and
laterdemonstratetheindividualresearchoutcomes.
QED is a relativistic quantum field theory, a quantum theory of photons with
electrons, and is considered the most successful accurate theory we have, e.g., to
explaintheLambshift,theanomalousmagneticmomentoftheelectrons,andsoon
usingtheFeynmandiagramtechniqueofthecovariantperturbationapproach.We
willelaboratethenon-perturbationapproachinthisbook.
ThisbookpresentsnewaspectsofQEDfrombasicphysicstophysicalchemistry
withmathematicalrigor.Topicscoveredincludespindynamics,chemicalreactiv-
ity,thedualCauchyproblem,andmore.Readersinterestedinmodernapplications
of quantum field theory in nano-, bio-, and open systems will enjoy learning how
theup-to-datequantumtheoryofradiationwithmatterworksintheworldofQED.
In particular, chemical ideas restricted now to nonrelativistic quantum theory are
showntobeunifiedandextendedtorelativisticquantumfieldtheorythatisbasicto
particlephysicsandcosmology:realizationofthenew-generationquantumtheory.
Readersareassumedtohaveabackgroundequivalenttoanundergraduatestudent’s
elementary knowledge in electromagnetism, quantum mechanics, chemistry, and
mathematics. This book makes use of abundant figures to help the reader grasp
ideasquickly,includesmanyequationstohelpthereadertofollowthelogicstep-
by-step, and provides an ample range of examples and references to facilitate
in-depthlearning.
I would like to thank Drs. Koichi Nakamura, Kentaro Doi, Masato Senami,
Kazuhide Ichikawa, Ludwik Komorowski, Piotr Ordon, Andrzej Sokalski, Paweł
Szarek, Irene Yarovsky, David Henry, Hansong Cheng, Akinori Fukushima, Yuji
v
vi Preface
Ikeda,HirooNozaki,MasahiroFukuda,andmembersoftheTachibanaLaboratory
in Kyoto University for their collaboration and producing some of the figures of
numericalcalculations.
Kyoto,Japan AkitomoTachibana
31August2016
Contents
1 BasicPhysicsofQED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 QEDandQuantumMechanics. . . . . . . . . . . . . . . . . . . . . 1
1.1.2 TheMostBeautifulScientificExperiment. . . . . . . . . . . . . 3
1.1.3 MysteryofQuantumMechanics. . . . . . . . . . . . . . . . . . . . 4
1.1.4 NewTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.5 SurveyofThisBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.6 QuickReviewoftheStandardTheoryofQED. . . . . . . . . 8
1.1.7 New-GenerationQuantumTheory. . . . . . . . . . . . . . . . . . 9
1.1.8 Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 RiggedQEDTheory. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 19
1.2.1 UnderlyingHistoryoftheRiggedQEDTheory. . . . . . . . . 19
1.2.2 BasicPhysicsoftheRiggedQEDTheory. . . . . . . . . . . . . 22
1.2.3 TheMaxwellEquations. . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.2.4 TheDirac–Schr€odingerEquations. . . . . . . . . . . . . . . . . . 25
1.2.5 ContinuityEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.6 TheLorentzForceandStressTensors. . . . . . . . . . . . . . . 28
1.2.7 SpinTorqueofElectron. . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.2.8 SpinVorticityofElectron. . . . . . . . . . . . . . . . . . . . . . . . 32
1.2.9 AngularMomentumofQED. . . . . . . . . . . . . . . . . . . . . . 34
1.3 PhenomenologyoftheRiggedQEDTheory. . . . . . . . . . . . . . . . 36
1.3.1 EnergyDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.3.2 ElectromagneticEnergyDensity
inMagnetodielectricMedia. . . . . . . . . . . . . . . . . . . . . . . 39
1.3.3 EffectiveChargeNumberofElectromigration. . . . . . . . .. 45
1.4 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.4.1 TorqueinAnalyticalExamples. . . . . . . . . . . . . . . . . . . . 47
1.4.2 TorqueinMolecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
vii
viii Contents
1.4.3 ElectromagneticPropertiesofMatter
inMagnetodielectricMedia. . . . . . . . . . . . . . . . . . . . . . . 58
1.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2 Energy-MomentumTensorofQED. . . . . . . . . . . . . . . . . . . . . . . . . 65
2.1 Energy-MomentumTensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.1.1 PrincipleofEquivalence. . . . . . . . . . . . . . . . . . . . . . . . . 65
2.1.2 TheMinkowskiSpace-Time. . . . . . . . . . . . . . . . . . . . . . 75
2.2 RiggedFieldTheory. . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . 79
2.2.1 RiggedQEDTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.2.2 PrimaryRiggedQEDTheory. . . . . . . . . . . . . . . . . . . . . . 81
2.3 SUGRAEnergy-MomentumTensor. . . . . . . . . . . . . . . . . . . . . . 82
2.3.1 StressTensor.. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. 82
2.3.2 Energy-MomentumTensor. . . . . . . . . . . . . . . . . . . . . . . 83
2.3.3 SUGRAFormalism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.4 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.4.1 RiggedQEDTheoryintheCurvedSpace-Time. . . . . . . . 90
2.4.2 TheMajoranaParticle. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.4.3 TheAtiyah–SingerIndexTheorem. . . . . . . . . . . . . . . . . . 92
2.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3 ChemicalIdeasofQED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1.1 PrimaryRiggedQEDTheory. . . . . . . . . . . . . . . . . . . . . . 97
3.1.2 ShapeVolumeofShellStructureandtheIntrinsic
ElectronicTransitionState. . . . . . . . . . . . . . . . . . . . . . . . 99
3.2 StressTensorandtheSpindleStructure. . . . . . . . . . . . . . . . . . . . 102
3.3 StressastheEnergyDensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3.1 LiquidCharacter:StandingWaveMode
ofTensionlessElectron. . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3.2 LiquidCharacter:PropagatingWaveMode
ofTensionlessElectron. . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.3.3 MixedCharacter:TheBlochWaveModeofTension
FiniteElectron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.3.4 SpindleStructureAlongtheReactionCoordinate. . . . . . . 113
3.3.5 TheGenericLewisPairFormationandtheNonclassical
BondOrder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.4 RegionalChemicalPotential. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.5 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.5.1 ChemicalBond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.5.2 NonclassicalBondOrderandRegional
ChemicalPotential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Contents ix
4 Alpha-OscillatorTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1 CanonicalQuantization. . .. . . . .. . . . .. . . .. . . . .. . . . .. . . .. 143
4.1.1 QEDHamiltonian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.1.2 ConventionalConservativeQEDHamiltonian. . . . . . . . . . 145
4.2 Alpha-OscillatorTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.2.1 Synchronization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.2.2 CausalityandInitialCondition. . . . . . . . . . . . . . . . . . . . . 147
4.2.3 ElectromagneticField. . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.2.4 Alpha-OscillatorAlgebra. . . . . . . . . . . . . . . . . . . . . . . . . 151
4.3 Double-SlitSpace-Time-ResolvedPredictionofQED. . . . . . . . . 157
4.3.1 TheFeynmanMystery. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.3.2 TheDualCauchyProblem. . . . . . . . . . . . . . . . . . . . . . . . 158
4.4 NormalMode. .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . 168
4.4.1 ParticlePicture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
4.4.2 ElectromagneticFieldRenormalization. . . . . . . . . . . . . . 168
4.4.3 TheDiracFieldRenormalization. . . . . . . . . . . . . . . . . . . 170
4.4.4 RenormalizedKetVectorandWaveFunction. . . . . . . . . . 172
4.4.5 FormalSolutionsofbzαðeωÞðtÞ. . . . . . . . . . . . . . . . . . . . . . 174
4.5 Discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Chapter 1
Basic Physics of QED
Abstract Basic physics of quantum electrodynamics (QED) is reviewed in com-
parisonwithquantummechanics.Underexternalsourceofelectromagneticfields,
charged particles can be accelerated by the Lorentz force. The Lorentz force is
compensatedbytensionatanypointoftheMinkowskispace-time. Thetensionis
given by the divergence of internal self-stress tensor. The antisymmetric compo-
nent ofthe stress tensor leads tospintorque anddrives timeevolutionofelectron
spin. This is called the quantum electron spin vorticity principle. The spin torque
canbecompensatedbyaforcecalledzetaforce.
Keywords Alpha-oscillator theory • Chirality • Double slit • Dual Cauchy
problem • Electromigration • Helicity • Measurement • Primary Rigged QED
theory • Principle of equivalence • Response • Rigged QED theory • Spin
torque • Spin vorticity • Spindle structure • Stress tensor • Tension • Zeta force •
Zetapotential
1.1 Introduction
1.1.1 QED and Quantum Mechanics
In the Einstein special theory of relativity, a measurement of an “event” α is
discussed on the Minkowski space-time. Let an event α be characterized in rela-
b
tivistic quantum field theory by a field operator Fðct,x,y,zÞ at the Minkowski
space-timecoordinates(ct,x,y,z)asshowninFig.1.1.Thisisthestandardframe-
work of QED. In quantum mechanics, however, more operators bx,by, and bz with
Fbðct,bx,by,bzÞarerequiredtodiscussthemeasurementproblem.
This additional expectation value problem of bx,by, and bz with Fbðct,bx,by,bzÞ in
quantummechanicsmaybeviewedas“theicingonthecake”fromthatinQED.In
QED,theCartesiancoordinatesx,y,andzaremerelythescaleininchesorcmfor
b
Fðct,x,y,zÞ and are not the objects of observation. In QED, the Cartesian coordi-
natesx,y,andzarenotobservablesnorcanonicalvariablesnoroperators.Sothatin
QED, we have no problem with the collapse of wave function nor classical
©SpringerNatureSingaporePteLtd.2017 1
A.Tachibana,NewAspectsofQuantumElectrodynamics,
DOI10.1007/978-981-10-3132-8_1