Dynamics of charged particles and their radiation field

378 Pages·2004·2.313 MB·English

by  Herbert Spohn

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DYNAMICS OF CHARGED PARTICLES AND THEIR
RADIATION FIELD
This book provides a self-contained and systematic introduction to classical elec-
trontheoryanditsquantizationnonrelativisticquantumelectrodynamics.Thefirst
halfofthebookcoverstheclassicaltheory.Itdiscussesthewell-definedAbraham
modelofextendedchargesininteractionwiththeelectromagneticfield,andgives
astudyoftheeffectivedynamicsofchargesundertheconditionthat,onthescale
givenbythesizeofthechargedistribution,theyarefarapartandtheappliedpoten-
tialsvaryslowly.Thesecondhalfcoversthequantumtheory,leadingtoacoherent
presentationofnonrelativisticquantumelectrodynamics.Topicsdiscussedinclude
nonperturbative properties of the basic Hamiltonian, the structure of resonances,
therelaxationtothegroundstatethroughemissionofphotons,thenonperturbative
derivationoftheg-factoroftheelectron,andthestabilityofmatter.
Suitable as a supplementary text for graduate courses, this book will also be
a valuable reference for researchers in mathematical physics, classical electrody-
namics,quantumoptics,andappliedmathematics.
HERBERT SPOHN is Professor of Mathematical Physics at Zentrum Mathe-
matik, Technische Universita¨t Mu¨nchen. He obtained his Ph.D. from Ludwig-
Maximilians-Universita¨t Mu¨nchen in 1975. He has done research at universities
andinstitutesthroughouttheworld.Hisresearchinterestsareinstatisticalphysics,
particularlydynamicsandnonequilibriumstatisticalmechanics,withonefocuson
thederivationofmacroscopicevolutionequationsfromthedynamicsofatoms.He
hashadnumerouspublicationsintheseareas.From2000to2002hehasbeenthe
presidentoftheInternationalAssociationofMathematicalPhysics.

DYNAMICS OF CHARGED PARTICLES
AND THEIR RADIATION FIELD
HERBERT SPOHN
TechnischeUniversita¨tMu¨nchen
cambridge university press
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Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521836975
© H. Spohn 2004
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2004
isbn-13 978-0-511-21079-2 eBook (EBL)
isbn-10 0-511-21256-9
eBook (EBL)
isbn-13 978-0-521-83697-5 hardback
isbn-10 0-521-83697-2 hardback
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for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
TothememoryofmyparentsOrtrudKnoppandKarlSpohn

Contents
Preface pagexi
Listofsymbols xiii
1 Scope,motivation,andorientation 1
PartI Classicaltheory 5
2 Achargecoupledtoitselectromagneticfield 7
2.1 TheinhomogeneousMaxwell–Lorentzequations 8
2.2 Newton’sequationsofmotion 12
2.3 CoupledMaxwell’sandNewton’sequations 13
2.4 TheAbrahammodel 17
2.5 TherelativisticallycovariantLorentzmodel 22
2.5.1 Thefour-currentdensity 24
2.5.2 Relativisticaction,equationsofmotion 27
3 Historicalnotes 33
3.1 Extendedchargemodels(1897–1912) 33
3.2 Nonrelativisticquantumelectrodynamics 36
3.3 Thepointcharge 37
3.4 Wheeler–Feynmanelectrodynamics 41
4 Theenergy–momentumrelation 44
4.1 TheAbrahammodel 44
4.2 TheLorentzmodel 48
4.3 Thelimitofzerobaremass 51
5 Long-timeasymptotics 54
5.1 Radiationdampingandtherelaxationoftheacceleration 55
5.2 Convergencetothesolitonmanifold 59
5.3 Scatteringtheory 61
vii
viii Contents
6 Adiabaticlimit 65
6.1 Scalinglimitforexternalpotentialsofslowvariation 66
6.1.1 Appendix 1: How small is ε?71
6.1.2 Appendix2:Adiabaticprotection 72
6.2 Comparisonwiththehydrodynamiclimit 74
6.3 Point-chargelimit,negativebaremass 75
7 Self-force 80
7.1 Memoryequation 81
7.2 Taylorexpansion 83
7.3 Howcantheaccelerationbebounded? 86
8 Comparisondynamics 91
8.1 Anexampleforsingularperturbationtheory 94
8.2 Thecriticalmanifold 95
8.3 Trackingofthetruesolution 97
8.4 Electromagneticfieldsintheadiabaticlimit 100
8.5 Larmor’sformula 101
9 TheLorentz–Diracequation 106
9.1 Criticalmanifold,theLandau–Lifshitzequation 107
9.2 Someapplications 109
9.3 ExperimentalstatusoftheLorentz–Diracequation 114
10 Spinningcharges 119
10.1 EffectivespindynamicsoftheLorentzmodel 119
10.2 TheAbrahammodelwithspin 121
10.3 Adiabaticlimitandthegyromagneticratio 125
11 Manycharges 130
11.1 Retardedinteraction 130
11.2 Limitofsmallvelocities 132
11.3 TheVlasov–Maxwellequations 138
11.4 Statisticalmechanics 139
12 Summaryandpreambletothequantumtheory 145
PartII Quantumtheory 147
13 QuantizingtheAbrahammodel 149
13.1 LagrangianandHamiltonianrewritingoftheAbrahammodel 150
13.2 ThePauli–FierzHamiltonian 153
13.3 Fockspace,self-adjointness 160
13.4 Energyandlengthscales 164
13.5 Conservationlaws 167
13.6 BoundaryconditionsandtheCasimireffect 169
13.7 Dipoleandsingle-photonapproximation 171