FINITE-TEMPERATURE FIELD THEORY Principles and Applications This book develops the basic formalism and theoretical techniques for study- ing relativistic quantum field theory at high temperature and density. Specific physical theories treated include QED, QCD, electroweak theory, and effective nuclear field theories of hadronic and nuclear matter. Topics include functional integral representation of the partition function, diagrammatic expansions, lin- ear response theory, screening and plasma oscillations, spontaneous symmetry breaking, the Goldstone theorem, resummation and hard thermal loops, lattice gaugetheory,phasetransitions,nucleationtheory,quark–gluonplasma,andcolor superconductivity. Applications to astrophysics and cosmology include white dwarf and neutron stars, neutrino emissivity, baryon number violation in the early universe, and cosmological phase transitions. Applications to relativistic nucleus–nucleus collisions are also included. JOSEPH I. KAPUSTA is Professor of Physics at the School of Physics and Astron- omy,UniversityofMinnesota,Minneapolis.HereceivedhisPh.D.fromtheUni- versity of California, Berkeley, in 1978 and has been a faculty member at the UniversityofMinnesotasince1982.Hehasauthoredover150articlesinrefereed journals and conference proceedings. Since 1997 he has been an associate editor for Physical Review C. He is a Fellow of the American Physical Society and of the American Association for the Advancement of Science. The first edition of Finite-Temperature Field Theory was published by Cambridge University Press in 1989; a paperback edition followed in 1994. CHARLESGALEisJamesMcGillProfessorattheDepartmentofPhysics,McGill University, Montreal. He received his Ph.D. from McGill University in 1986 and joined the faculty there in 1989. He has authored over 100 articles in refereed journals and conference proceedings. Since 2005 he has been the Chair of the Department of Physics at McGill University. He is a Fellow of the American Physical Society. CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS General editors: P. V. Landshoff, D. R. Nelson, S. Weinberg S.CarlipQuantum Gravity in 2+1 Dimensions† J.C.CollinsRenormalization† M.CreutzQuarks, Gluons and Lattices† P.D.D’EathSupersymmetric Quantum Cosmology† F.deFeliceandC.J.S.ClarkeRelativity on Curved Manifolds† B.S.DeWittSupermanifolds,secondedition† P.G.O.FreundIntroduction to Supersymmetry† J.FuchesAffine Lie Algebras and Quantum Groups† J.FuchsandC.SchweigertSymmetries, Lie Algebras and Representations: A Graduate Course for Physicists† Y.FujiiandK.MaedaThe Scalar–Tensor Theory of Gravitation A.S.Galperin,E.A.Ivanov,V.I.OrievetskyandE.S.SokatchevHarmonic Superspace† R.GambiniandJ.PullinLoops, Knots, Gauge Theories and Quantum Gravity† M.Go¨ckelerandT.Schu¨ckerDifferential Geometry, Gauge Theories and Gravity† C.G´omez,M.RuizAltabaandG.SierraQuantum Groups in Two-Dimensional Physics† M.B.Green,J.H.SchwarzandE.WittenSuperstring Theory, Volume 1: Introduction† M.B.Green,J.H.SchwarzandE.WittenSuperstring Theory, Volume 1: 2: Loop Amplitudes, Anomalies and Phenomenology† V.N.GribovThe Theory of Complex Angular Momenta S.W.HawkingandG.F.R.EllisThe Large Scale Structure of Space–Time† F.IachelloandA.ArimaThe Interacting Boson Model F.IachelloandP.vanIsackerThe Interacting Boson–Fermion Model† C.ItzyksonandJ.-M.DrouffeStatistical Field Theory, Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory† C.ItzyksonandJ.-M.DrouffeStatistical Field Theory, Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems† C.JohnsonD-Branes J.I.KapustaandC.Gale,Finite-Temperature Field Theory V.E.Korepin,N.M.BoguliubovandA.G.IzerginThe Quantum Inverse Scattering Method and Correlation Functions† M.LeBellacThermal Field Theory† Y.MakeenkoMethods of Contemporary Gauge Theory† N.MantonandP.SutcliffeTopological Solitons N.H.MarchLiquid Metals: Concepts and Theory† I.M.MontvayandG.Mu¨nsterQuantum Fields on a Lattice† L.O’RaifeartaighGroup Structure of Gauge Theories† T.Ort´ınGravity and Strings A.OzoriodeAlmeidaHamiltonian Systems: Chaos and Quantization† R.PenroseandW.RindlerSpinors and Space-Time, Volume 1: Two-Spinor Calculus and Relativistic Fields† R.PenroseandW.RindlerSpinorsandSpace-Time,Volume2:SpinorandTwistorMethods in Space-Time Geometry† S.PokorskiGauge Field Theories, second edition† J.PolchinskiString Theory, Volume 1: An Introduction to the Bosonic String† J.PolchinskiString Theory, Volume 2: Superstring Theory and Beyond† V.N.PopovFunctional Integrals and Collective Excitations† R.J.RiversPath Integral Methods in Quantum Field Theory† R.G.RobertsThe Structure of the Proton† C.RoveliQuantum Gravity W.C.SaslawGravitational Physics of Stellar Galactic Systems† H.Stephani,D.Kramer,M.A.H.MacCallum,C.HoenselaersandE.HerltExact Solutions of Einstein’s Field Equations, second edition J.M.StewartAdvanced General Relativity† A.VilenkinandE.P.S.ShellardCosmic Strings and Other Topological Defects† R.S.WardandR.O.WellsJrTwister Geometry and Field Theory† J.R.WilsonandG.J.MathewsRelativistic Numerical Hydrodynamics 1Issuedasapaperback Finite-Temperature Field Theory Principles and Applications JOSEPH I. KAPUSTA School of Physics and Astronomy, University of Minnesota CHARLES GALE Department of Physics, McGill University cambridge university press Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,S˜aoPaulo CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB22RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521820820 (cid:2)C J.I.KapustaandC.Gale2006 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithout thewrittenpermissionofCambridgeUniversityPress. Firstpublished1989 Firstpaperbackedition1994 Secondedition2006 PrintedintheUnitedKingdomattheUniversityPress,Cambridge A catalog record for this publication is available from the British Library ISBN-13 978-0-521-82082-0hardback ISBN-10 0-521-82082-0hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLsfor externalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnot guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate. Contents Preface page ix 1 Review of quantum statistical mechanics 1 1.1 Ensembles 1 1.2 One bosonic degree of freedom 3 1.3 One fermionic degree of freedom 5 1.4 Noninteracting gases 6 1.5 Exercises 10 Bibliography 11 2 Functional integral representation of the partition function 12 2.1 Transition amplitude for bosons 12 2.2 Partition function for bosons 15 2.3 Neutral scalar field 16 2.4 Bose–Einstein condensation 19 2.5 Fermions 23 2.6 Remarks on functional integrals 30 2.7 Exercises 31 Reference 31 Bibliography 31 3 Interactions and diagrammatic techniques 33 3.1 Perturbation expansion 33 3.2 Diagrammatic rules for λφ4 theory 34 3.3 Propagators 38 3.4 First-order corrections to Π and lnZ 41 3.5 Summation of infrared divergences 45 3.6 Yukawa theory 47 v vi Contents 3.7 Remarks on real time perturbation theory 51 3.8 Exercises 53 References 54 Bibliography 54 4 Renormalization 55 4.1 Renormalizing λφ4 theory 55 4.2 Renormalization group 57 4.3 Regularization schemes 60 4.4 Application to the partition function 61 4.5 Exercises 63 References 63 Bibliography 63 5 Quantum electrodynamics 64 5.1 Quantizing the electromagnetic field 64 5.2 Blackbody radiation 68 5.3 Diagrammatic expansion 70 5.4 Photon self-energy 71 5.5 Loop corrections to lnZ 74 5.6 Exercises 82 References 83 Bibliography 83 6 Linear response theory 84 6.1 Linear response to an external field 84 6.2 Lehmann representation 87 6.3 Screening of static electric fields 90 6.4 Screening of a point charge 94 6.5 Exact formula for screening length in QED 97 6.6 Collective excitations 100 6.7 Photon dispersion relation 101 6.8 Electron dispersion relation 105 6.9 Kubo formulae for viscosities and conductivities 107 6.10 Exercises 114 References 115 Bibliography 115 7 Spontaneous symmetry breaking and restoration 117 7.1 Charged scalar field with negative mass-squared 117 7.2 Goldstone’s theorem 123 7.3 Loop corrections 125 7.4 Higgs model 130 Contents vii 7.5 Exercises 133 References 133 Bibliography 134 8 Quantum chromodynamics 135 8.1 Quarks and gluons 136 8.2 Asymptotic freedom 139 8.3 Perturbative evaluation of partition function 146 8.4 Higher orders at finite temperature 149 8.5 Gluon propagator and linear response 152 8.6 Instantons 156 8.7 Infrared problems 161 8.8 Strange quark matter 163 8.9 Color superconductivity 166 8.10 Exercises 174 References 175 Bibliography 176 9 Resummation and hard thermal loops 177 9.1 Isolating the hard thermal loop contribution 179 9.2 Hard thermal loops and Ward identities 185 9.3 Hard thermal loops and effective perturbation theory 187 9.4 Spectral densities 188 9.5 Kinetic theory 189 9.6 Transport coefficients 193 9.7 Exercises 194 References 194 10 Lattice gauge theory 195 10.1 Abelian gauge theory 196 10.2 Nonabelian gauge theory 202 10.3 Fermions 203 10.4 Phase transitions in pure gauge theory 206 10.5 Lattice QCD 212 10.6 Exercises 217 References 217 Bibliography 218 11 Dense nuclear matter 219 11.1 Walecka model 220 11.2 Loop corrections 226 11.3 Three- and four-body interactions 232 11.4 Liquid–gas phase transition 233 viii Contents 11.5 Summary 236 11.6 Exercises 237 References 238 Bibliography 239 12 Hot hadronic matter 240 12.1 Chiral perturbation theory 240 12.2 Self-energy from experimental data 248 12.3 Weinberg sum rules 254 12.4 Linear and nonlinear σ models 265 12.5 Exercises 287 References 287 Bibliography 288 13 Nucleation theory 289 13.1 Quantum nucleation 290 13.2 Classical nucleation 294 13.3 Nonrelativistic thermal nucleation 296 13.4 Relativistic thermal nucleation 298 13.5 Black hole nucleation 313 13.6 Exercises 315 References 315 Bibliography 316 14 Heavy ion collisions 317 14.1 Bjorken model 318 14.2 The statistical model of particle production 324 14.3 The emission of electromagnetic radiation 328 14.4 Photon production in high-energy heavy ion collisions 331 14.5 Dilepton production 339 14.6 J/ψ suppression 345 14.7 Strangeness production 350 14.8 Exercises 356 References 358 Bibliography 359 15 Weak interactions 361 15.1 Glashow–Weinberg–Salam model 361 15.2 Symmetry restoration in mean field approximation 365 15.3 Symmetry restoration in perturbation theory 369 15.4 Symmetry restoration in lattice theory 374 15.5 Exercises 377 References 377 Bibliography 378 Contents ix 16 Astrophysics and cosmology 379 16.1 White dwarf stars 380 16.2 Neutron stars 382 16.3 Neutrino emissivity 388 16.4 Cosmological QCD phase transition 394 16.5 Electroweak phase transition and baryogenesis 402 16.6 Decay of a heavy particle 408 16.7 Exercises 410 References 411 Bibliography 412 Conclusion 413 Appendix 417 A1.1 Thermodynamic relations 417 A1.2 Microcanonical and canonical ensembles 418 A1.3 High-temperature expansions 421 A1.4 Expansion in the degeneracy 423 References 424 Index 425