Quantum gravity

406 Pages·2012·5.093 MB·English

by  Kiefer, Claus

INTERNATIONAL SERIES OF MONOGRAPHS
ON PHYSICS
SERIES EDITORS
J. BIRMAN CITY UNIVERSITY OF NEW YORK
S. F. EDWARDS UNIVERSITY OF CAMBRIDGE
R. FRIEND UNIVERSITY OF CAMBRIDGE
M. REES UNIVERSITY OF CAMBRIDGE
D. SHERRINGTON UNIVERSITY OF OXFORD
G. VENEZIANO CERN, GENEVA
International Series of Monographs on Physics
155.C.Kiefer:Quantumgravity,Thirdedition
154.L.Mestel:Stellarmagnetism,Secondedition
153.R.A.Klemm:Layeredsuperconductors, Volume1
152.E.L.Wolf:Principlesofelectrontunnelingspectroscopy, Secondedition
151.R.Blinc:Advancedferroelectricity
150.L.Berthier,G.Biroli,J.-P.Bouchaud,W.vanSaarloos,L.Cipelletti:Dynamical heterogeneitiesin
glasses,colloidsandgranularmedia
149.J.Wesson:Tokamaks, Fourthedition
148.H.Asada,T.Futamase,P.Hogan:Equationsofmotion ingeneralrelativity
147.A.Yaouanc,P.DalmasdeR´eotier:Muonspinrotation,relaxation,andresonance
146.B.McCoy:Advancedstatistical mechanics
145.M.Bordag,G.L.Klimchitskaya,U.Mohideen,V.M.Mostepanenko:AdvancesintheCasimireffect
144.T.R.Field:Electromagneticscatteringfromrandommedia
143.W.Go¨tze:Complexdynamicsofglass-formingliquids–amode-couplingtheory
142.V.M.Agranovich:Excitationsinorganicsolids
141.W.T.Grandy:Entropyandthetimeevolutionofmacroscopic systems
140.M.Alcubierre:Introduction to3+1numericalrelativity
139.A.L.Ivanov,S.G.Tikhodeev:Problemsofcondensedmatterphysics–quantumcoherence
phenomenainelectron–holeandcoupledmatter–light systems
138.I.M.Vardavas,F.W.Taylor:Radiation andclimate
137.A.F.Borghesani:Ionsandelectronsinliquidhelium
135.V.Fortov,I.Iakubov,A.Khrapak:Physicsofstronglycoupledplasma
134.G.Fredrickson:Theequilibriumtheoryofinhomogeneous polymers
133.H.Suhl:Relaxationprocesses inmicromagnetics
132.J.Terning:Modernsupersymmetry
131.M.Marin˜o:Chern–Simons theory,matrixmodels,andtopological strings
130.V.Gantmakher:Electronsanddisorderinsolids
129.W.Barford:Electronicandoptical properties ofconjugatedpolymers
128.R.E.Raab,O.L.deLange:Multipole theoryinelectromagnetism
127.A.Larkin,A.Varlamov:Theoryoffluctuationsinsuperconductors
126.P.Goldbart,N.Goldenfeld,D.Sherrington:Stealingthegold
125.S.Atzeni,J.Meyer-ter-Vehn:Thephysicsofinertialfusion
123.T.Fujimoto:Plasmaspectroscopy
122.K.Fujikawa,H.Suzuki:Pathintegralsandquantumanomalies
121.T.Giamarchi:Quantumphysics inonedimension
120.M.Warner,E.Terentjev:Liquidcrystalelastomers
119.L.Jacak,P.Sitko,K.Wieczorek,A.Wojs:QuantumHallsystems
117.G.Volovik:TheUniverseinaheliumdroplet
116.L.Pitaevskii,S.Stringari:Bose–Einstein condensation
115.G.Dissertori,I.G.Knowles,M.Schmelling:Quantumchromodynamics
114.B.DeWitt:Theglobalapproach toquantumfieldtheory
113.J.Zinn-Justin:Quantumfieldtheoryandcriticalphenomena,Fourthedition
112.R.M.Mazo:Brownian motion–fluctuations,dynamics,andapplications
111.H.Nishimori:Statistical physicsofspinglassesandinformation processing –anintroduction
110.N.B.Kopnin:Theoryofnonequilibriumsuperconductivity
109.A.Aharoni:Introduction tothetheoryofferromagnetism, Secondedition
108.R.Dobbs:Heliumthree
107.R.Wigmans:Calorimetry
106.J.Ku¨bler:Theoryofitinerantelectronmagnetism
105.Y.Kuramoto,Y.Kitaoka:Dynamicsofheavyelectrons
104.D.Bardin,G.Passarino:TheStandardModelinthemaking
103.G.C.Branco,L.Lavoura,J.P.Silva:CPViolation
102.T.C.Choy:Effectivemediumtheory
101.H.Araki:Mathematical theoryofquantumfields
100.L.M.Pismen:Vorticesinnonlinearfields
98.K.H.Bennemann:Nonlinearopticsinmetals
94.S.Chikazumi:Physicsofferromagnetism
91.R.A.Bertlmann:Anomaliesinquantumfieldtheory
90.P.K.Gosh:Iontraps
87.P.S.Joshi:Globalaspects ingravitation andcosmology
86.E.R.Pike,S.Sarkar:Thequantumtheoryofradiation
83.P.G.deGennes,J.Prost:Thephysics ofliquidcrystals
73.M.Doi,S.F.Edwards:Thetheoryofpolymerdynamics
69.S.Chandrasekhar:Themathematical theoryofblackholes
51.C.Møller:Thetheoryofrelativity
46.H.E.Stanley:Introduction tophasetransitions andcriticalphenomena
32.A.Abragam:Principlesofnuclearmagnetism
27.P.A.M.Dirac:Principlesofquantummechanics
23.R.E.Peierls:Quantumtheoryofsolids
Quantum Gravity
Third Edition
Claus Kiefer
Institute for Theoretical Physics
University of Cologne
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Preface to the Third Edition
Inmythirdedition,Ihaverevisedthetextinmanyplacesthroughoutthebook.Onthe
onehand,Ihavespentconsiderableeffortonimprovingitsconceptualstructureandits
pedagogicalaspects.Ontheotherhand,Ihaveupdatedandextendedthepresentation
of the topics discussed in the earlier editions and added new material on topics such
as primordialblack holes,black holesin accelerators,singularityavoidance,quantum-
gravity phenomenology, string field theory, and Hoˇrava–Lifshits gravity. Whenever
possible, I have shown the links between the various approaches to quantum gravity.
Asinthepreviouseditions,theemphasiswasonwritinganintroductoryandcoherent
text and not an encyclopedia of all existing approaches.
I thank all the readers who have commented on various parts of the earlier edi-
tions or who have pointed out the occurrence of typos. Comments would be greatly
appreciatedalsofor the thirdedition. They canbe senttomy e-mailaddresskiefer@
thp.uni-koeln.de.
For helpful discussions and critical comments while preparing the third edition,
I owe my thanks to Julian Barbour, Andrei Barvinsky, Martin Bojowald, Bianca
Dittrich, Domenico Giulini, Herbert Hamber, Friedrich Hehl, Manuel Kra¨mer, Claus
La¨mmerzahl, Renate Loll, Paulo Vargas Moniz, Hermann Nicolai, Marcel Reginatto,
MartinReuter,MarkRoberts,ChristianSteinwachs,KurtSundermeyer,StefanThei-
sen,andH.-DieterZeh.IamgratefulinparticulartoJulianBarbourforgoingthrough
thewholesecondeditionwithmeandmakingnumerousinvaluablesuggestionsforim-
provingstyleandconceptualclarity.IalsothanktheMaxPlanckInstituteforGravita-
tionalPhysics(Albert EinsteinInstitute), Potsdam,forits kindhospitalitywhile part
of the work on the new edition was done. I have also profited much from discussions
on historical aspects of quantum-gravity researchat the Max Planck Institute for the
History of Science, Berlin, and I thank Ju¨rgen Renn for giving me this opportunity.
As before, I want to thank Oxford University Press for their most efficient co-
operation.
Cologne Claus Kiefer
January 2012
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Preface to the Second Edition
The constructionof a consistenttheory of quantumgravitycontinuesto be the major
open problem in fundamental physics. The present second edition of my book is an
extendedandrevisedversionofthefirstedition.Itcontains,inparticular,newsections
onasymptoticsafety,dynamicaltriangulation,primordialblackholes,theinformation-
loss problem, loop quantum cosmology, and other topics. The text has been revised
throughout.
Ithankallthe readerswhohavecommentedonvariouspartsofthe firsteditionor
whohavepointedouttheoccurrenceoftypos.Commentswouldbegreatlyappreciated
also for the second edition. They can be sent to my e-mail address
[email protected].
For helpful discussions and critical comments while preparing the second edition
I am grateful to Mark Albers, Andrei Barvinsky, Martin Bojowald, Friedrich Hehl,
Gerhard Kolland, Renate Loll, Hermann Nicolai, Martin Reuter, Barbara Sandho¨fer,
Stefan Theisen, and H.-Dieter Zeh.
LastbutnotleastIwanttothankOxfordUniversityPress,andinparticularSonke
Adlung, for their efficient cooperation.
Cologne Claus Kiefer
December 2006
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Preface
The unification of quantum theory with Einstein’s theory of general relativity is per-
hapsthebiggestopenproblemoftheoreticalphysics.Suchatheoryisnotonlyneeded
for conceptual reasons, but also for the understanding of fundamental issues such as
the origin of the Universe, the final evaporation of black holes, and the structure of
space and time.
Historically, the oldest approach is the direct quantization of Einstein’s theory
of general relativity, an approach which is still being actively pursued. This includes
covariantmethodssuchaspath-integralquantizationaswellascanonicalmethodslike
the Wheeler–DeWitt approach or the more recent loop quantization. Although one
arrives at a perturbatively non-renormalizabletheory, quantum general relativity can
yield physically interesting results in both the perturbative and the non-perturbative
regimes. It casts light, in particular, on the fundamental nature of space and time.
Thesecondmainapproachis stringtheory.Itencapsulatesthe ideathatthe prob-
lem of constructing a viable quantum theory of gravity can only be solved within a
unification of all interactions. In this respect, it goes far beyond quantum generalrel-
ativity. From a methodological point of view, however, string theory does not stand
much apart from it. It is a natural extension of perturbative quantum gravity (from
whichit inherits the conceptofa graviton),andmethods of constrainedquantization,
which are crucial for canonical quantum gravity, appear at key stages in the theory.
Whereas there exist excellent textbooks that discuss string theory at great depth,
the present monograph is the first that, to my knowledge, covers quantum gravity in
this broadsense. The mainpartof the book is devotedto generalconcepts,the quan-
tization of general relativity, and applications to cosmology and black holes. String
theoryisdiscussedfromthe pointofview ofits quantumgravitationalaspectsandits
connectiontootherapproaches.Theedificeoftheoreticalphysicscannotbecompleted
without the conceptual unification that will be provided by quantum gravity. I hope
that my book will convince my readers of this outstanding problem and encourage
them to work on its solution.
This book has grown out of lectures that I gave at the Universities of Zu¨rich,
Freiburg, and Cologne between 1990 and 2003. My main intention is to discuss the
general features that a quantum theory of gravity is expected to show and to give
an up-to-date overview of the main approaches. The reader is assumed to have some
familiaritywithgeneralrelativityandquantumfieldtheory.Commentscanbe sentto
my e-mail address [email protected] are highly welcome.