A Philosophical Approach to Quantum Field Theory

275 Pages·2018·5.223 MB·English

by  Hans Christian Öttinger

A PHILOSOPHICAL APPROACH TO
QUANTUM FIELD THEORY
This text presents an intuitive and robust mathematical image of fundamental
particle physics based on a novel approach to quantum field theory, which is
guided by four carefully motivated metaphysical postulates. In particular, the
book explores a dissipative approach to quantum field theory, which is illustrated
for scalar field theory and quantum electrodynamics and proposes an attractive
explanation of the Planck scale in quantum gravity. Offering a radically new
perspective on this topic, the book focuses on the conceptual foundations of
quantum field theory and ontological questions. It also suggests a new stochastic
simulation technique in quantum field theory, which is complementary to existing
ones. Encouraging rigor in a field containing many mathematical subtleties and
pitfalls, this text is a helpful companion for students of physics and philosophers
interested in quantum field theory, and it allows readers to gain an intuitive rather
thanaformalunderstanding.
hans christian o¨ttinger is Professor of Polymer Physics at ETH Zu¨rich.
His research is focused on developing a general framework of nonequilibrium
thermodynamicsasatoolfordescribingdissipativeclassicalandquantumsystems.

A PHILOSOPHICAL APPROACH TO
QUANTUM FIELD THEORY
HANS CHRISTIAN O¨ TTINGER
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DOI:10.1017/9781108227667
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Names:O¨ttinger,HansChristian,1958–author.
Title:Aphilosophicalapproachtoquantumfieldtheory/HansChristianO¨ttinger
(SwissFederalInstituteofTechnology,Zu¨rich).
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversityPress,2017.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2017035063|
ISBN9781108415118(Hardback;alk.paper)|ISBN1108415113(Hardback;alk.paper)
Subjects:LCSH:Quantumfieldtheory.|Physics–Philosophy.|Knowledge,Theoryof.
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Contents
Preface pagexi
Acknowledgments xiii
1 ApproachtoQuantumFieldTheory 1
1.1 PhilosophicalContemplations 2
1.1.1 ImagesofNature 3
1.1.2 SpaceandTime 11
1.1.3 Infinity 19
1.1.4 Irreversibility 23
1.1.5 OntheMeasurementProblem 34
1.1.6 ApproachestoQuantumFieldTheory 38
1.2 MathematicalandPhysicalElements 49
1.2.1 FockSpace 50
1.2.2 Fields 55
1.2.3 Dynamics 57
1.2.4 QuantitiesofInterest 69
1.2.5 Renormalization 76
1.2.6 Symmetries 87
1.2.7 Expansions 89
1.2.8 Unravelings 92
1.2.9 Summary 103
2 ScalarFieldTheory 110
2.1 SomeBasicEquations 111
2.1.1 FreeDissipativeEvolution 111
2.1.2 PerturbationTheory 113
2.2 Propagator 115
2.2.1 Second-OrderPerturbationExpansion 116
2.2.2 GoingtotheLimits 121
vii
viii Contents
2.2.3 RelativisticCovariance 126
2.2.4 OnShellRenormalization 129
2.3 VertexFunction 132
2.3.1 Four-TimeCorrelationFunctions 133
2.3.2 APrimaryCorrelationFunction 134
2.3.3 CoreCorrelationFunctions 137
2.4 SummaryandDiscussion 138
3 QuantumElectrodynamics 141
3.1 TheDiracEquation 142
3.1.1 WaveEquationsforFreeParticles 143
3.1.2 RelativisticCovariance 144
3.1.3 PlanarWaveSolutions 146
3.1.4 InteractionwithElectromagneticFields 150
3.1.5 From3+1to1+1Dimensions 151
3.2 MathematicalImageofQuantumElectrodynamics 153
3.2.1 FockSpace 153
3.2.2 Fields 156
3.2.3 HamiltonianandCurrentDensity 159
3.2.4 SchwingerTerm 162
3.2.5 BRSTQuantization 163
3.2.6 QuantumMasterEquation 174
3.3 SchwingerModel 176
3.3.1 FockSpace 177
3.3.2 Fields 178
3.3.3 HamiltonianandCurrentDensity 180
3.3.4 SchwingerTerm 182
3.3.5 BRSTQuantization 182
3.3.6 ExactSolution 184
3.3.7 FermionsandBosonsinOneSpaceDimension 191
3.4 ConfrontationwiththeRealWorld 197
3.4.1 FreePropagators 198
3.4.2 ScatteringProblems 200
3.4.3 MagneticMomentoftheElectron 210
4 Perspectives 220
4.1 TheNatureofQuantumFieldTheory 220
4.1.1 TheImage 220
4.1.2 ImplicationsforOntology 222
4.2 OpenMathematicalProblems 225
4.3 FutureDevelopments 227
Contents ix
AppendixA AnEfficientPerturbationScheme 229
AppendixB PropertiesofDiracMatrices 239
AppendixC Baker–Campbell–HausdorffFormulas 241
References 243
Indexes
AuthorIndex 251
SubjectIndex 254