Quantum Field Theory and Gravity: Conceptual and Mathematical ...

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Quantum Field Theoryand GravityConceptual and Mathematical Advancesin the Search for a Unified FrameworkFelix FinsterOlaf MüllerMarc NardmannJürgen TolksdorfEberhard ZeidlerEditors
Edito rsFelix FinsterLehrstuhl für MathematikUniversität RegensburgGermanyMarc NardmannFachbereich MathematikUniversität HamburgGermanyOlaf MüllerLehrstuhl für MathematikUniversität RegensburgGermanyJürgen TolksdorfMax-Planck-Institut fürMathematik in den NaturwissenschaftenLeipzig, GermanyEberhard ZeidlerMax-Planck-Institut fürMathematik in den NaturwissenschaftenLeipzig, GermanyISBN 978-3-0348-0042- 6 e-ISBN 978-3-0348-0043-3DOI 10.1007/978-3-0348-0043-3Springer Basel Dordrecht Heidelberg London New YorkLibrary of Congress Control Number: 2012930975Mathematical Subject Classification (2010): 81-06, 83-06© Springer Basel AG 2012This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,reproduction on microfilms or in other ways, and storage in data banks. For any kind of use, permissionof the copyright owner must be obtained.Printed on acid-free paperSpringer Basel AG is part of Springer Science + Business Mediawww.birkhauser-science.com
Page 6 and 7: ContentsPreface ...................
Page 8 and 9: PrefaceThe present volume arose fro
Page 10 and 11: Prefaceix6. (How) can we test quant
Page 12 and 13: PrefacexiFelix Finster, Andreas Gro
Page 14 and 15: Prefacexiiiit is related to other a
Page 16 and 17: Quantum Gravity: Whence, Whither?Cl
Page 18 and 19: Quantum Gravity: Whence, Whither? 3
Page 28: Quantum Gravity: Whence, Whither? 1
Page 31 and 32: 16 K. Fredenhagen and K. Rejznerfie
Page 34 and 35: Local Covariance and Background Ind
Page 36 and 37: Local Covariance and Background Ind
Page 38: Local Covariance and Background Ind
Page 41 and 42: 26 B. TempleIn [14] the authors int
Page 43 and 44: 28 B. TempleTheorem 2.1. Assume p =
Page 45 and 46: 30 B. Templeconservation laws will
Page 47 and 48: 32 B. Templeas to why small-scale o
Page 49 and 50: 34 B. Temple5) How did you reach th
Page 51 and 52: 36 B. Temple9) How large would the
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38 B. Temple13) If Dark Energy does
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40 B. Temple[6] J. Glimm, P.D. Lax,
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42 S. Gielen and D. OritiIn this co
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44 S. Gielen and D. Oritimultiplica
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46 S. Gielen and D. Oritiway that c
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48 S. Gielen and D. Oriti⃗p g on
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50 S. Gielen and D. OritiUsing the
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52 S. Gielen and D. Orititopology a
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54 S. Gielen and D. Oritiand to mak
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56 S. Gielen and D. OritiC 2i 2j 2j
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58 S. Gielen and D. Oritiwhich one
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60 S. Gielen and D. Oritiradical, f
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62 S. Gielen and D. OritiReferences
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64 S. Gielen and D. Oriti[42] Aleja
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66 A. Döring and R. Soares Barbosa
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98 J. L. Flores, J. Herrera and M.
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Some Mathematical Aspects of the Ha
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Hawking Effect for Rotating Black H
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Observables in theGeneral Boundary
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Observables in the General Boundary
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4. QuantizationObservables in the G
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Causal Fermion Systems:A Quantum Sp
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Causal Fermion Systems 159We have t
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Causal Fermion Systems 1611.2.1. Fr
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Causal Fermion Systems 163The space
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Causal Fermion Systems 165property
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Causal Fermion Systems 1671.3. An a
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2. Spontaneous structure formationC
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Causal Fermion Systems 171We next c
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Causal Fermion Systems 1733.2. A ti
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Causal Fermion Systems 175In order
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Causal Fermion Systems 177Figure 1.
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Causal Fermion Systems 179allow τ
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ReferencesCausal Fermion Systems 18
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CCR- versus CAR-Quantization on Cur
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On the Notion of ‘the Same Physic
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The Same Physics in All Spacetimes
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230 R. VerchThe basic idea of local
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232 R. VerchThe conditions LCSE-1..
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234 R. Verchfor the just defined st
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236 R. Verchquantum fields in curve
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238 R. Verch(i) Let D be a subset o
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240 R. VerchFigure 1. Sketch of tem
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242 R. VerchStructure of the set of
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244 R. Verchare referred to as symm
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246 R. Verch(δ) Finally we mention
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248 R. Verchsuch that ω β(x) (ϑ(
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250 R. Vercha state with respect to
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252 R. Verchif such solutions could
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254 R. Verchproperties of quantum f
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256 R. Verch[35] A. Strohmaier, R.
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258 J. Barbourtheory. My aim in thi
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260 J. Barbourrelative to each othe
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262 J. BarbourFigure 2. In Newtonia
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264 J. BarbourFive more data are ne
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266 J. Barboursignal is generated u
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268 J. Barbouraba b cFigure 4. a) A
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270 J. BarbourFigure 5. The action
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272 J. BarbourFigure 6. The disting
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274 J. Barbourbe expressed through
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276 J. BarbourIn this connection, l
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278 J. Barbourthey leave all length
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280 J. BarbourSlicings of spacetime
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282 J. Barbourdefinition, structure
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284 J. Barbourwould indicate a spur
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286 J. Barbourwhole idea: general r
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288 J. Barbourother variables. It i
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290 J. Barbourgeometrodynamics is V
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292 J. Barboura straight line at a
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294 J. Barbouroccur in dynamics. Ei
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296 J. Barbour[7] J Barbour. The Di
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On the Motion of Point Defects inRe
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On the Motion of Point Defects in R
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338 S. Hollandsasymptotically flat
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340 S. HollandsIn the case where Σ
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342 S. HollandsThe black hole horiz
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344 S. Hollands[18] Hollands, S., I
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346 D. Giuliniwell either fail to h
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348 D. Giulinitaken along different
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350 D. GiuliniM2. The trajectories
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352 D. Giulinias that of test parti
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354 D. Giulinione, since the energi
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356 D. Giuliniacceleration is just
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358 D. GiuliniThe time evolution of
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360 D. Giuliniwith ĥ := h/f, so th
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362 D. Giulinitransferring momentum
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364 D. GiuliniThe calculation of (5
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366 D. Giuliniin which the left-han
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368 D. Giulini6. ConclusionI conclu
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370 D. Giulini[26] Pippa Storey and
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372 IndexBose-Einstein condensate,
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374 Indexentropy flux density, 242E
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376 Indexloop order (of diagram), 4
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378 Indexgravitational, 2Reeh-Schli
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380 IndexUV, see ultravioletvacuum,
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