Approaches to fundamental physics: an assessment of current theoretical ideas PDF
Preview Approaches to fundamental physics: an assessment of current theoretical ideas
Lecture 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. 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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
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