You have just completed your registration at OpenAire.
Before you can login to the site, you will need to activate your account.
An e-mail will be sent to you with the proper instructions.
Important!
Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version
of the site upon release.
We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity $\Im^+$. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to $\Im^+$. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos, is imposed. We review its definition critically showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant under the action of all spacetime isometries exists and it is explicitly constructed.
[AM82] A. Ashtekar and A. Magnon-Ashtekar, “On the Symplectic Structure of General Relativity,” Commun. Math. Phys. 86, 55 (1982).
[Ash81] A. Ashtekar, “Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity,” J. Math. Phys. 22 (1981) 2885.
[BDH13] M. Benini, C. Dappiaggi and T. -P. Hack, “Quantum Field Theory on Curved Backgrounds - A Primer,” Int. J. Mod. Phys. A 28 (2013) 1330023 [arXiv:1306.0527 [gr-qc]].
[BDHS13] M. Benini, C. Dappiaggi, T. -P. Hack and A. Schenkel, “A C*-algebra for quantized principal U(1)-connections on globally hyperbolic Lorentzian manifolds,” to appear in Communications in Mathematical Physics [arXiv:1307.3052 [math-ph]],
[BDS12] M. Benini, C. Dappiaggi and A. Schenkel, “Quantum field theory on affine bundles,” Annales Henri Poincare 15 (2014) 171 [arXiv:1210.3457 [math-ph]].
[BDS13] M. Benini, C. Dappiaggi and A. Schenkel, “Quantized Abelian principal connections on Lorentzian manifolds,” to appear in Communications in Mathematical Physics [arXiv:1303.2515 [math-ph]].
[DL12] C. Dappiaggi and B. Lang,“Quantization of Maxwell's equations on curved backgrounds and general local covariance,” Lett. Math. Phys. 101 (2012) 265 [arXiv:1104.1374 [gr-qc]].
[DMP05] C. Dappiaggi, V. Moretti and N. Pinamonti, “Rigorous steps towards holography in asymptotically flat spacetimes,” Rev. Math. Phys. 18 (2006) 349 [gr-qc/0506069].
[DMP07] C. Dappiaggi, V. Moretti and N. Pinamonti, “Cosmological horizons and reconstruction of quantum field theories,” Commun. Math. Phys. 285 (2009) 1129 [arXiv:0712.1770 [gr-qc]].
[DMP09] C. Dappiaggi, V. Moretti and N. Pinamonti, “Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property,” J. Math. Phys. 50 (2009) 062304.
[DMP11] C. Dappiaggi, V. Moretti and N. Pinamonti, “Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime,” Adv. Theor. Math. Phys. 15 (2011) 355 [arXiv:0907.1034 [gr-qc]].
[DPP11] C. Dappiaggi, N. Pinamonti and M. Porrmann, “Local causal structures, Hadamard states and the principle of local covariance in quantum field theory,” Commun. Math. Phys. 304 (2011) 459 [arXiv:1001.0858 [hep-th]].
[DS13] C. Dappiaggi and D. Siemssen, “Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes,” Rev. Math. Phys. 25, 1350002 (2013) [arXiv:1106.5575 [gr-qc]].
[FH12] C. J. Fewster and D. S. Hunt, “Quantization of linearized gravity in cosmological vacuum spacetimes,” Rev. Math. Phys. 25, 1330003 (2013) [arXiv:1203.0261 [math-ph]].
[FNW81] S. A. Fulling, F. J. Narcowich and R. M. Wald, “Singularity Structure of the Two Point Function in Quantum Field Theory in Curved Space-time. II,” Annals Phys. 136 (1981) 243.
[FS13] F. Finster and A. Strohmaier, “Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times,” arXiv:1307.1632 [math-ph].
[Fro79] V. P. Frolov, “Null Surface Quantization And Quantum Theory Of Massless Fields In Asymptotically Flat Space-time,” Gen. Rel. Grav. 10 (1979) 833.
[FV13] C. J. Fewster and R. Verch, “The Necessity of the Hadamard Condition,” Class. Quant. Grav. 30 (2013) 235027 [arXiv:1307.5242 [gr-qc]].
[GW14a] C. G´erard and M. Wrochna, “Construction of Hadamard states by pseudo-differential calculus,” Commun. Math. Phys. 325 (2014) 713 [arXiv:1209.2604 [math-ph]].
[GW14b] C. G´erard and M. Wrochna, “Hadamard states for the linearized Yang-Mills equation on curved spacetime,” [arXiv:1403.7153 [math-ph]].
[Hac14] T. -P. Hack, “Quantization of the linearised Einstein-Klein-Gordon system on arbitrary backgrounds and the special case of perturbations in Inflation,” arXiv:1403.3957 [gr-qc].
[HS12] T. -P. Hack and A. Schenkel, “Linear bosonic and fermionic quantum gauge theories on curved spacetimes,” Gen. Rel. Grav. 45, 877 (2013) [arXiv:1205.3484 [math-ph]].
[HI03] S. Hollands and A. Ishibashi, “Asymptotic flatness and Bondi energy in higher dimensional gravity,” J. Math. Phys. 46 (2005) 022503 [gr-qc/0304054].
[Ho00] S. Hollands, “Aspects of Quantum Field Theory in Curved Spacetime”. Ph.D.thesis, University of York, 2000, advisor B.S. Kay.
[HW14] S. Hollands and R. M. Wald, “Quantum fields in curved spacetime,” [arXiv:1401.2026 [gr-qc]].
[Hor90] L. H¨ormander The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, Berlin, Heidelberg, New York: Springer, 2nd edn., (1990).
[Hun12] D. S. Hunt, “The Quantization of Linear Gravitational Perturbations and the Hadamard Condition,” PhD thesis, (2012) University of York, available here.
[KW88] B. S. Kay and R. M. Wald, “Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon,” Phys. Rept. 207, 49 (1991).
[Kha12] I. Khavkine, “Characteristics, Conal Geometry and Causality in Locally Covariant Field Theory,” arXiv:1211.1914 [gr-qc].
[Kha14b] I. Khavkine, “Cohomology with causally restricted supports,” arXiv:1404.1932 [mathph].
[Mar93] D. M. Marolf, “The Generalized Peierls bracket,” Annals Phys. 236, 392 (1994) [hepth/9308150].
[Mor05] V. Moretti, “Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence,” Commun. Math. Phys. 268 (2006) 727 [gr-qc/0512049].
[Mor06] V. Moretti, “Quantum out-states holographically induced by asymptotic flatness: Invariance under spacetime symmetries, energy positivity and Hadamard property,” Commun. Math. Phys. 279 (2008) 31 [gr-qc/0610143].
[Mur13] S. Murro, “Hadamard states for linearized gravity on asymptotically flat spacetimes”, MSc thesis, University of Pavia (2013).
[Pei52] R. E. Peierls, “The Commutation laws of relativistic field theory,” Proc. Roy. Soc. Lond. A 214, 143 (1952).
[San13] K. Sanders, “A note on spacelike and timelike compactness,” Class. Quant. Grav. 30 (2013) 115014 [arXiv:1211.2469 [math-ph]].
[SDH12] K. Sanders, C. Dappiaggi and T. -P. Hack, “Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law,” to appear in Communications in Mathematical Physics [arXiv:1211.6420 [math-ph]].
[Sie11] D. Siemssen, “Quantization of the electromagnetic cally flat spacetimes,” Diploma thesis (2011) Universita¨t http://www.desy.de/uni-th/theses/Dipl_Siemssen.pdf