Quantum Gowdy T3 model: A uniqueness result

Classical and Quantum Gravity

Volumn 23, Issue 22, 2006, Pages

  Corichi, Alejandro ^a,b   Cortez, Jerónimo ^c   Mena Marugán, Guillermo A ^c   Velhinho, José M ^d  

^a INSTITUTO DE MATEMÁTICAS   (Mexico)

^b INSTITUTO DE CIENCIAS NUCLEARES   (Mexico)

^c INSTITUTO DE ESTRUCTURA DE LA MATERIA   (Spain)

^d UNIVERSITY OF BEIRA INTERIOR   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846156897     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/22/014     Document Type: Article

References (36)

1. Wald R M 1994 Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Chicago, IL: Chicago University Press)
2. Simon B 1972 Topics in Functional Analysis ed R F Streater (London: Academic)
3. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53
4. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
5. Thiemann T 2001 Introduction to modern canonical quantum general relativity Preprint gr-qc/0110034
6. Lewandowski J, Okolow A, Sahlmann H and Thiemann T 2005 Uniqueness of diffeomorphism invariant states on holonomy-flux algebras Preprint gr-qc/0504147
7. See e.g. Corichi A, Cortez J and Quevedo H 2004 Schrödinger and Fock representation for a field theory on curved spacetime Ann. Phys. 313 446
8. Ashtekar A and Magnon A 1975 Quantum fields in curved space-times Proc. R. Soc. A 346 375
9. Ashtekar A and Magnon-Ashtekar A 1980 A curiosity concerning the role of coherent states in quantum field theory Pramana 15 107
10. Misner C W 1972 Minisuperspace Magic Without Magic: John Archibald Wheeler ed J Klauder (San Francisco: Freeman)
11. Torre C G 1999 Midisuperspace models of canonical quantum gravity Int. J. Theor. Phys. 38 1081
12. Corichi A, Cortez J and Mena Marugán G A 2006 Unitary evolution in Gowdy cosmology Phys. Rev. D 73 041502
13. 3 model: a unitary description Phys. Rev. D 73 084020
14. Gowdy R H 1974 Vacuum space-times with two parameter spacelike isometry groups and compact invariant hypersurfaces: topologies and boundary conditions Ann. Phys. 83 203
15. 3 cosmology Phys. Rev. D 8 3271
16. Berger B K 1974 Quantum graviton creation in a model universe Ann. Phys. 83 458
17. 3 model Phys. Rev. D 11 2770
18. 3 cosmology Ann. Phys. 156 155
19. Husain V and Smolin L 1989 Exactly solvable quantum cosmologies from two Killing field reductions of general relativity Nucl. Phys. B 327 205
20. Mena Marugán G A 1997 Canonical quantization of the Gowdy model Phys. Rev. D 56 908
21. Pierri M 2002 Probing quantum general relativity through exactly soluble midi-superspaces. II: polarized Gowdy models Int. J. Mod. Phys. D 11 135
22. 3 cosmologies Int. J. Mod. Phys. D 11 1451
23. 3 cosmological model Phys. Rev. D 72 064020
24. 3 model Phys. Rev. D 66 084017
25. Jacobson T 1991 Unitarity, causality and quantum gravity Conceptual Problems of Quantum Gravity ed A Ashtekar and J Stachel (Cambridge, MA: Birkhäuser Boston)
26. Kramer D, Stephani H, MacCallum M and Herlt E 1980 Exact Solutions of Einstein's Field Equations (Cambridge: Cambridge University Press)
27. Cho D H J and Varadarajan M 2006 Functional evolution of quantum cylindrical waves Preprint gr-qc/0605065
28. Abramowitz M and Stegun I A (ed) 1970 Handbook of Mathematical Functions 9th edn (Washington DC: US Govt. Print Off.) (Nat. Bur. Stand. Appl. Math. Ser. No. 55)
29. See e.g. Choquet-Bruhat Y, DeWitt-Morette C and Dillard-Bleick M 1996 Analysis, Manifolds and Physics, Part I: Basics (Amsterdam: Elsevier)
30. Kay B S 1978 Linear spin-zero quantum fields in external gravitational and scalar fields. I: a one particle structure for the stationary case Commun. Math. Phys. 62 55
31. Shale D 1962 Linear symmetries of free boson fields Trans. Am. Math. Soc. 103 149
32. Honegger R and Rieckers A 1996 Squeezing Bogoliubov transformations on the infinite CCR-algebra J. Math. Phys. 37 4292
33. Kolmogorov A N and Fomin S V 1999 Elements of the Theory of Functions and Functional Analysis (New York: Dover)
34. Reed M and Simon B 1975 Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointeness (San Diego: Academic)
35. Mourão J M, Thiemann T and Velhinho J M 1999 Physical properties of quantum field theory measures J. Math. Phys. 40 2337
36. Ashtekar A and Magnon-Ashtekar A 1980 A geometrical approach to external potential problems in quantum field theory Gen. Rel. Grav. 12 205