Table Of ContentLecture Notes in Physics
EditorialBoard
R.Beig,Wien,Austria
W.Beiglböck,Heidelberg,Germany
W.Domcke,Garching,Germany
B.-G.Englert,Singapore
U.Frisch,Nice,France
P.Hänggi,Augsburg,Germany
G.Hasinger,Garching,Germany
K.Hepp,Zürich,Switzerland
W.Hillebrandt,Garching,Germany
D.Imboden,Zürich,Switzerland
R.L.Jaffe,Cambridge,MA,USA
R.Lipowsky,Potsdam,Germany
H.v.Löhneysen,Karlsruhe,Germany
I.Ojima,Kyoto,Japan
D.Sornette,Nice,France,andZürich,Switzerland
S.Theisen,Potsdam,Germany
W.Weise,Garching,Germany
J.Wess,München,Germany
J.Zittartz,Köln,Germany
TheLectureNotesin Physics
TheseriesLectureNotesinPhysics(LNP),foundedin1969,reportsnewdevelopments
in physics research and teaching – quickly and informally, but with a high quality and
theexplicitaimtosummarizeandcommunicatecurrentknowledgeinanaccessibleway.
Bookspublishedinthisseriesareconceivedasbridgingmaterialbetweenadvancedgrad-
uatetextbooksandtheforefrontofresearchandtoservethreepurposes:
(cid:129) tobeacompactandmodernup-to-datesourceofreferenceonawell-definedtopic
(cid:129) to serve as an accessible introduction to the field to postgraduate students and
nonspecialistresearchersfromrelatedareas
(cid:129) tobeasourceofadvancedteachingmaterialforspecializedseminars,coursesand
schools
Both monographs and multi-author volumes will be considered for publication. Edited
volumes should, however, consist of a very limited number of contributions only. Pro-
ceedingswillnotbeconsideredforLNP.
VolumespublishedinLNParedisseminatedbothinprintandinelectronicformats,the
electronicarchivebeingavailableatspringerlink.com.Theseriescontentisindexed,ab-
stractedandreferencedbymanyabstractingandinformationservices,bibliographicnet-
works,subscriptionagencies,librarynetworks,andconsortia.
ProposalsshouldbesenttoamemberoftheEditorialBoard,ordirectlytothemanaging
editoratSpringer:
ChristianCaron
SpringerHeidelberg
PhysicsEditorialDepartmentI
Tiergartenstrasse17
69121Heidelberg/Germany
[email protected]
Ion-Olimpiu Stamatescu
Erhard Seiler (Eds.)
Approaches
to Fundamental Physics
An Assessment of Current Theoretical Ideas
ABC
Editors
Ion-OlimpiuStamatescu ErhardSeiler
ForschungsstättederEvangelischen Max-Planck-InstitutfürPhysik
Studiengemeinschaft(FESt) Werner-Heisenberg-Institut
Schmeilweg5 80805München,Germany
69118Heidelberg,Germany [email protected]
and
InstitutfürTheoretischePhysik
UniversitätHeidelberg
Philosophenweg16
69120Heidelberg,Germany
[email protected]
I.-O.StamatescuandE.Seiler(Eds.),ApproachestoFundamental Physics,Lect.Notes
Phys.721(Springer,BerlinHeidelberg2007),DOI10.1007/978-3-540-71117-9
LibraryofCongressControlNumber:2007923173
ISSN0075-8450
ISBN978-3-540-71115-5 SpringerBerlinHeidelbergNewYork
Thisworkissubjecttocopyright. Allrightsarereserved, whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,
1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations
areliableforprosecutionundertheGermanCopyrightLaw.
SpringerisapartofSpringerScience+BusinessMedia
springer.com
(cid:2)c Springer-VerlagBerlinHeidelberg2007
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,
evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws
andregulationsandthereforefreeforgeneraluse.
Typesetting:bytheauthorsandIntegrausingaSpringerLATEXmacropackage
Coverdesign:eStudioCalamarS.L.,F.Steinen-Broo,Pau/Girona,Spain
Printedonacid-freepaper SPIN:12026159 543210
Preface
This book representsin the firstplace the desireof the authorsofthe various
contributions to enter a discussion about the research landscape of present-
dayfundamentaltheoreticalphysics.Itdocuments their attempt, outoftheir
highly specialized scientific positions, to find a way of communicating about
methods,achievements,andpromisesofthedifferentapproacheswhichshape
the development of this field. It is therefore also an attempt to bring out
the connections between these approaches, and present them not as disjoint
ventures but rather as facets of a common quest for understanding.
Whether in competition to each other or in collaboration, the ‘many-fold
ways’ of contemporary physics are characterized by a number of exciting
findings (andquestions)whichappearmoreandmoreinterrelated.Moreover,
in the historical development of science, the steadily arriving new empiri-
cal information partly supports, partly contradicts the existing theories, and
partlybringsforthunexpectedresultsforcingatotalreorientationuponus.If
we are lucky, the beginning of this century may prove to be as grand as that
of the last one.
It is not an easy task in a situation so much in movement and in which
variousapproachesstriveforcompletion,topromoteaconstructiveinteraction
between these and to achieve a level of mutual understanding on which such
an interaction can be fruitful. Nearly all of the authors contributing to this
book have been participating in a working group dedicated exactly to this
task; this group met in many sessions over several years. This book is to a
large extent the result of these discussions.
The support of the authors’ home institutions was of course important
for this project, but one institution has to be singled out for making this
book possible: this is FESt, Heidelberg (Forschungssta¨tte der Evangelischen
Studiengemeinschaft – Protestant Institute for Interdisciplinary Research).
FESt has a long tradition in bringing together interdisciplinary working
groups. In particular, it has cultivated the dialogue between the natural sci-
ences, philosophy, theology, and the life sciences – but also projects inside
one discipline which involve discussion across the specialized fields and aim
VI Preface
at a more general understanding of fundamental questions pertaining to this
discipline. Our work has constituted a FESt project belonging to this class.
The intention of working groups at FESt typically is not only to present
the differing perspectives but also to compare them and to find relations
which could be fruitful for the fields involved.To achieve this goal,numerous
group sessions are required and FESt provides hereto a unique scientific and
organizational environment. This has been extremely useful for our project
and we are very grateful to FESt for its support of our work as well as its
continuous interest and confidence in it.
We appreciateverymuchthe interestofSpringer-Verlaginpromotingthe
interdisciplinary exchangeofinformationat the levelof specialists.We thank
Wolf Beiglb¨ock for excellent advice and assistance in the completion of the
book and the Springer team for dedicated editorial and publishing work.
Hans-Gu¨nter Dosch
Ju¨rgen Ehlers
Klaus Fredenhagen
Domenico Giulini
Claus Kiefer
Oliver Lauscher
Jan Louis
Thomas Mohaupt
Hermann Nicolai
Kasper Peeters
Karl-Henning Rehren
Martin Reuter
Michael G. Schmidt
Erhard Seiler
Ion-Olimpiu Stamatescu
Norbert Straumann
Stefan Theisen
Heidelberg, September 2006 Thomas Thiemann
Contents
Part I Introduction
Introduction – The Many-Fold Way of Contemporary
High Energy Theoretical Physics
E. Seiler, I.-O. Stamatescu........................................ 3
1 Historical Remarks ........................................... 5
2 Systematic Considerations..................................... 7
3 Conceptual Questions......................................... 14
Part II Elementary Particle Theory
The Standard Model of Particle Physics
H. G. Dosch..................................................... 21
1 Introduction ................................................. 21
2 The Development of the Standard Model ....................... 21
3 Systematic Description of the Standard Model ................... 29
4 Achievements and Deficiencies of the Standard Model............. 37
5 Extrapolationto the Near Future .............................. 46
6 Conclusion .................................................. 48
Literature....................................................... 49
Beyond the Standard Model
M. G. Schmidt .................................................. 51
Selected References............................................... 56
Part III Quantum Field Theory
Quantum Field Theory: Where We Are
K. Fredenhagen, K.-H. Rehren, and E. Seiler ........................ 61
1 Introduction ................................................. 61
2 Axiomatic Approaches to QFT................................. 62
VIII Contents
3 The Gauge Principle.......................................... 67
4 The Field Concept ........................................... 69
5 The Perturbative Approach to QFT ............................ 71
6 The Constructive Approach to QFT ............................ 73
7 Effective Quantum Field Theories .............................. 77
8 Gravity ..................................................... 79
9 Conclusions and Outlook...................................... 84
References ...................................................... 85
Part IV General Relativity Theory
General Relativity
J. Ehlers........................................................ 91
1 Introduction ................................................. 91
2 Basic Assumptions of GRT .................................... 93
3 General Comments on the Structure of GRT..................... 97
4 Theoretical Developments, Achievements and Problems in GRT .... 99
Selected References...............................................103
Remarks on the Notions of General Covariance
and Background Independence
D. Giulini.......................................................105
1 Introduction .................................................105
2 Attempts to Define General Covariance
and/or BackgroundIndependence ..............................106
3 Conclusion ..................................................118
References ......................................................119
Part V Quantum Gravity
Why Quantum Gravity?
C. Kiefer .......................................................123
References ......................................................130
The Canonical Approach to Quantum Gravity:
General Ideas and Geometrodynamics
D. Giulini and C. Kiefer..........................................131
1 Introduction .................................................131
2 The Initial-Value Formulation of GR............................133
3 Why Constraints .............................................134
4 Comparisonwith Conventional
Form of Einstein’s Equations ..................................135
5 Canonical Gravity............................................138
6 The General Kinematics of Hypersurface Deformations............140
Contents IX
7 TopologicalIssues ............................................141
8 Geometric Issues .............................................144
9 Quantum Geometrodynamics ..................................145
10 Applications .................................................148
References ......................................................150
Loop and Spin Foam Quantum Gravity:
A Brief Guide for Beginners
H. Nicolai and K. Peeters.........................................151
1 Quantum Einstein Gravity ....................................151
2 The Kinematical Hilbert Space of LQG .........................154
3 Area, Volume, and the Hamiltonian.............................157
4 Implementation of the Constraints..............................160
5 Quantum Space-Time Covariance?..............................164
6 Canonical Gravity and Spin Foams .............................167
7 Spin Foam Models: Some Basic Features ........................171
8 Spin Foams and Discrete Gravity...............................175
9 Predictive (Finite) Quantum Gravity? ..........................178
References ......................................................180
Loop Quantum Gravity: An Inside View
T. Thiemann....................................................185
1 Introduction .................................................185
2 Classical Preliminaries ........................................189
3 Canonical Quantisation Programme ............................193
4 Status of the Quantisation Programme for Loop
Quantum Gravity (LQG)......................................198
5 Physical Applications .........................................236
6 Conclusions and Outlook......................................244
References ......................................................254
Quantum Einstein Gravity: Towards an Asymptotically
Safe Field Theory of Gravity
O. Lauscher and M. Reuter .......................................265
1 Introduction .................................................265
2 Asymptotic Safety............................................266
3 RG Flow of the Effective Average Action........................268
4 Scale-Dependent Metrics and the Resolution
Function (cid:2)(k) ................................................272
5 Microscopic Structure of the QEG Spacetimes ...................276
6 The Spectral Dimension.......................................279
7 Concluding Remarks..........................................283
References ......................................................283
X Contents
Part VI String Theory
String Theory: An Overview
J. Louis, T. Mohaupt, and S. Theisen ..............................289
1 Introduction .................................................289
2 Beyond the Standard Model ...................................290
3 The Free String ..............................................293
4 The Interacting String ........................................297
5 Compactification .............................................299
6 Duality and M-Theory ........................................302
7 AdS/CFT ...................................................305
8 Black-Hole Entropy...........................................309
9 Approaches to Phenomenology.................................315
10 Open Questions ..............................................319
11 Some Concluding Remarks ....................................321
Selected References...............................................322
Part VII Cosmology
Dark Energy
N. Straumann ...................................................327
1 Introduction .................................................327
2 Einstein’s Original Motivation of the Λ-Term ....................328
3 From Static to Expanding World Models ........................330
4 The Mystery of the Λ-Problem.................................334
5 Luminosity–Redshift Relation for Type Ia Supernovae.............340
6 MicrowaveBackground Anisotropies ............................349
7 ObservationalResults and Cosmological Parameters ..............355
8 Alternatives to Dark Energy ...................................359
A Essentials of Friedmann–Lemaˆıtre Models .......................366
B Thermal History below 100 MeV ...............................374
C Inflation and Primordial Power Spectra .........................379
D Quintessence Models..........................................391
References ......................................................393
Appendix
K.-H. Rehren and E. Seiler........................................399
1 Quantum Theory.............................................399
2 Field Theory.................................................400
