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

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Local Thermal Equilibrium and Cosmology 255 [13] C.J. Fewster, A general worldline quantum inequality, Class. Quantum Grav. 17 (2000) 1897 [14] C.J. Fewster, Energy inequalities in quantum field theory, in: J. Zambrini (ed.), Proceedings of the XIV International Congress on Mathematical Physics, Lisbon, 2003, World Scientific, Singapore, 2005. e-Print: arXiv:math-ph/0501073 [15] C.J. Fewster and L. Osterbrink, Quantum energy inequalities for the nonminimally coupled scalar field, J. Phys. A41(2008) 025402 [16] C.J. Fewster and C.J. Smith, Absolute quantum energy inequalities in curved spacetime, Ann. Henri Poincaré 9 (2008) 425 [17] M. Gransee, Diploma Thesis, Institute of Theoretical Physics, University of Leipzig, 2010 [18] A. Knospe, M. Gransee and R. Verch, in preparation [19] R. Haag, Local quantum physics, 2nd ed., Springer-Verlag, Berlin-Heidelberg- New York, 1996 [20] S. Hollands, Renormalized quantum Yang-Mills fields in curved spacetime, Rev. Math. Phys. 20 (2008) 1033 [21] S. Hollands and G. Leiler, On the derivation of the Boltzmann equation in quantum field theory: flat spacetime, e-Print: arXiv:1003.1621 [cond-mat.statmech] [22] S. Hollands and R.M. Wald, Local Wick polynomials and time ordered products of quantum fields in curved space-time, Commun. Math. Phys. 223 (2001) 289 [23] Kay, B.S. and Wald, R.M., Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on space-times with a bifurcate Killing horizon, Phys. Rep. 207 (1991) 49 [24] A. Knospe, Diploma Thesis, Institute of Theoretical Physics, University of Leipzig, 2010 [25] F. Lindner and R. Verch, to be published [26] N. Pinamonti, On the initial conditions and solutions of the semiclassical Einstein equations in a cosmological scenario, e-Print: arXiv:1001.0864 [gr-qc] [27] N. Pinamonti and R. Verch, in preparation [28] M.J. Radzikowski, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys. 179 (1996) 529 [29] K. Sanders, Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime, Commun. Math. Phys. 295 (2010) 485 [30] J. Schlemmer, PhD Thesis, Faculty of Physics, University of Leipzig, 2010 [31] J. Schlemmer, Local thermal equilibrium states and Unruh detectors in quantum field theory, e-Print: hep-th/0702096 [hep-th] [32] J. Schlemmer and R. Verch, Local thermal equilibrium states and quantum energy inequalities, Ann. Henri Poincaré 9 (2008) 945 [33] C. Solveen, Local thermal equilibrium in quantum field theory on flat and curved spacetimes, Class. Quant. Grav. 27 (2010) 235002 [34] A. Starobinski, A new type of isotropic cosmological models without singularity, Phys. Lett. B91 (1980) 99
256 R. Verch [35] A. Strohmaier, R. Verch and M. Wollenberg, Microlocal analysis of quantum fields on curved spacetimes: analytic wavefront sets and Reeh-Schlieder theorems, J. Math. Phys. 43 (2002) 5514 [36] R. Verch, A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework, Commun. Math. Phys. 223 (2001) 261 [37] R.M. Wald, The back reaction effect in particle creation in curved spacetime, Commun. Math. Phys. 54 (1977) 1 [38] R.M. Wald, Trace anomaly of a conformally invariant quantum field in curved space-time, Phys. Rev. D17 (1978) 1477 [39] R.M. Wald, General relativity, University of Chicago Press, Chicago, 1984 [40] R.M. Wald, Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, Chicago, 1994 [41] R.M. Wald, Existence of the S matrix in quantum field theory in curved spacetime, Ann. Physics (N.Y.) 118 (1979) 490 [42] S. Weinberg, Cosmology, Oxford University Press, Oxford, 2008 Rainer Verch Institut für Theoretische Physik Universität Leipzig Vor dem Hospitaltore 1 D-04103 Leipzig Germany e-mail: verch@itp.uni-leipzig.de
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Quantum Field Theory and Gravity Co
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Contents Preface ..................
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Preface The present volume arose fr
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Preface ix 6. (How) can we test qua
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Preface xi Felix Finster, Andreas G
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Preface xiii it is related to other
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Quantum Gravity: Whence, Whither? C
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Quantum Gravity: Whence, Whither? 3
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16 K. Fredenhagen and K. Rejzner fi
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18 K. Fredenhagen and K. Rejzner Th
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20 K. Fredenhagen and K. Rejzner 4.
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22 K. Fredenhagen and K. Rejzner 5.
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The “Big Wave” Theory for Dark
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Discrete and Continuum Third Quanti
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Unsharp Values, Domains and Topoi A
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Unsharp Values, Domains and Topoi 6
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Causal Boundary of Spacetimes: Revi
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Causal Boundaries 99 to the Gromov
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Causal Boundaries 101 I + (ρ) ρ P
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Causal Boundaries 103 Figure 2. The
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Causal Boundaries 105 more pairings
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Causal Boundaries 107 point of the
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Causal Boundaries 109 (0, 1) x n x
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Causal Boundaries 111 to Busemann f
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Causal Boundaries 113 respectively.
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Causal Boundaries 115 6.3. Structur
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Causal Boundaries 117 Qualitative F
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Causal Boundaries 119 [26] E. Mingu
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122 D. Häfner Let us give an idea
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124 D. Häfner Figure 1. The collap
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126 D. Häfner Figure 2. The manifo
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128 D. Häfner and the angular mome
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130 D. Häfner Lemma 3.5. There exi
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132 D. Häfner Proposition 4.4. The
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134 D. Häfner 6. Strategy of the p
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136 D. Häfner [3] B. Carter, Black
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138 R. Oeckl it is less compelling
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140 R. Oeckl Depending on the theor
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142 R. Oeckl 2.3. Recovery of stand
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144 R. Oeckl where the condition A
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146 R. Oeckl Before we proceed to i
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148 R. Oeckl the complex classical
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150 R. Oeckl The corresponding anni
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152 R. Oeckl Proposition 4.1 (Coher
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154 R. Oeckl much larger than the s
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156 R. Oeckl Setting F equal to F
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158 F. Finster, A. Grotz and D. Sch
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184 C. Bär and N. Ginoux treat the
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186 C. Bär and N. Ginoux the categ
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188 C. Bär and N. Ginoux Example 2
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190 C. Bär and N. Ginoux 3.2. Diff
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192 C. Bär and N. Ginoux In other
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194 C. Bär and N. Ginoux Here (e j
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196 C. Bär and N. Ginoux Remark 3.
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198 C. Bär and N. Ginoux Proof. Th
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200 C. Bär and N. Ginoux To prove
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202 C. Bär and N. Ginoux We refer
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Page 231 and 232: 216 C. J. Fewster ϕ(ψ) M M ϕ(M)(
Page 233 and 234: 218 C. J. Fewster theory. The resul
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Page 237 and 238: 222 C. J. Fewster Sketch of proof.
Page 239 and 240: 224 C. J. Fewster The relative Cauc
Page 241 and 242: 226 C. J. Fewster [2] Bär, C., Gin
Page 244 and 245: Local Covariance, Renormalization A
Page 246 and 247: Local Thermal Equilibrium and Cosmo
Page 272 and 273: Shape Dynamics. An Introduction Jul
Page 274 and 275: Shape Dynamics. An Introduction 259
Page 284 and 285: where dx bm a Shape Dynamics. An In
Page 312: Shape Dynamics. An Introduction 297
Page 315 and 316: 300 M. Kiessling In the following,
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306 M. Kiessling (2.17) and (2.18)
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308 M. Kiessling Maxwell’s “law
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310 M. Kiessling argued that E f (
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312 M. Kiessling the Maxwell-Born-I
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314 M. Kiessling removal. For insta
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316 M. Kiessling ∂ 4πc that for
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318 M. Kiessling d dt Dirac, on the
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320 M. Kiessling The Lorenz-Lorentz
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322 M. Kiessling ( 1 c Lorentz and
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324 M. Kiessling potential fields
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326 M. Kiessling as I have done her
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328 M. Kiessling just the Hamilton-
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330 M. Kiessling 7. Closing remarks
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332 M. Kiessling [Bor1937] Born, M.
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334 M. Kiessling [Lié1898] Liénar
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How Unique Are Higher-dimensional B
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Equivalence Principle, Quantum Mech
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Atom Interferometry 347 The second
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Atom Interferometry 349 α CR , aim
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Atom Interferometry 351 of this mas
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Atom Interferometry 353 height B A
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Atom Interferometry 355 iff ψ = (
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Atom Interferometry 357 have be rea
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Atom Interferometry 359 where F (t
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Atom Interferometry 361 5.2. Interf
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Atom Interferometry 363 Evaluating
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Atom Interferometry 365 where the l
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Atom Interferometry 367 Then they s
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Atom Interferometry 369 [8] T.M. Fo
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Index n-point function, 51, 146, 23
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Index 373 conformal field theory, 1
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Index 375 gravitational redshift, 2
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Index 377 operator product, 138 par
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Index 379 standard model of particl
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