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Journal of Mathematical Physics
Volumn 50, Issue 1, 2009, Pages
Are the spectra of geometrical operators in loop quantum gravity really discrete?
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EID: 59349098629     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3054277     Document Type: Article
Times cited : (70)
References (17)
  • 1
    • 37349043730 scopus 로고    scopus 로고
    • An introduction to loop quantum gravity through cosmology
    • Nuovo Cimento B 0369-3554, ();, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/21/15/R01 21, R53 (2004), e-print arXiv:gr-qc/0404018;, " Introduction to looquantum gravity and spin foams," e-print arXiv:gr-qc/0409061;, (Cambridge University Press, Cambridge, 2004);, " How far are we from the quantum theory of gravity?," e-print arXiv:hep-th/0303185;, " An invitation to looquantum gravity," Lect. Notes Phys. 0075-8450 10.1007/978-3-540-71117-9-10 721, 185 (2007).;, " Lectures on looquantum gravity," Lect. Notes Phys. 0075-8450 631, 41 (2003);, Lect. Notes Phys. 631, 41 (2003), e-print arXiv:gr-qc/0210094;, (Cambridge University Press, Cambridge, 2007); e-print arXiv:gr-qc/0110034.
    • A. Ashtekar, " An introduction to loop quantum gravity through cosmology.," Nuovo Cimento B 0369-3554 122, 135 (2007); A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/21/15/R01 21, R53 (2004), e-print arXiv:gr-qc/0404018; A. Perez, " Introduction to loop quantum gravity and spin foams.," e-print arXiv:gr-qc/0409061; C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004); L. Smolin, " How far are we from the quantum theory of gravity?," e-print arXiv:hep-th/0303185; L. Smolin, " An invitation to loop quantum gravity.," Lect. Notes Phys. 0075-8450 10.1007/978-3-540-71117-9-10 721, 185 (2007).; T. Thiemann, " Lectures on loop quantum gravity.," Lect. Notes Phys. 0075-8450 631, 41 (2003); T. Thiemann, Lect. Notes Phys. 631, 41 (2003), e-print arXiv:gr-qc/0210094; T. Thiemann, Introduction to Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007); e-print arXiv:gr-qc/0110034.
    • (2007) Quantum Gravity, Introduction to Modern Canonical Quantum General Relativity , vol.122 , pp. 135
    • Ashtekar, A.1    Ashtekar, A.2    Lewandowski, J.3    Perez, A.4    Rovelli, C.5    Smolin, L.6    Smolin, L.7    Thiemann, T.8    Thiemann, T.9    Thiemann, T.10
  • 2
    • 33750083705 scopus 로고
    • 0550-3213 10.1016/0550-3213(95)00150-Q, ();, Nucl. Phys. B 0550-3213 10.1016/0550-3213(95)00550-5 456, 753 (E) (1995), e-print arXiv:gr-qc/9411005.
    • C. Rovelli and L. Smolin, Nucl. Phys. B 0550-3213 10.1016/0550-3213(95) 00150-Q 442, 593 (1995); C. Rovelli and L. Smolin, Nucl. Phys. B 0550-3213 10.1016/0550-3213(95)00550-5 456, 753 (E) (1995), e-print arXiv:gr-qc/9411005.
    • (1995) Nucl. Phys. B , vol.442 , pp. 593
    • Rovelli, C.1    Smolin, L.2    Rovelli, C.3    Smolin, L.4
  • 3
    • 0001979597 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/14/1A/006, (), e-print arXiv:gr-qc/9602046;, Adv. Theor. Math. Phys. 1095-0761 1, 388 (1998), e-print arXiv:gr-qc/9711031;, Class. Quantum Grav.
    • A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/14/1A/006 14, A55 (1997), e-print arXiv:gr-qc/9602046; A. Ashtekar and J. Lewandowski, Adv. Theor. Math. Phys. 1095-0761 1, 388 (1998), e-print arXiv:gr-qc/9711031; A. Ashtekar, A. Corichi, and J. A. Zapata, Class. Quantum Grav.
    • (1997) Class. Quantum Grav. , vol.14 , pp. 55
    • Ashtekar, A.1    Lewandowski, J.2    Ashtekar, A.3    Lewandowski, J.4    Ashtekar, A.5    Corichi, A.6    Zapata, J.A.7
  • 4
    • 0001979597 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/9/6/004, (), e-print arXiv:hep-th/9202053;, J. Math. Phys. 0022-2488 10.1063/1.531037 36, 2170 (1995), e-print arXiv:gr-qc/9411046.
    • A. Ashtekar and C. J. Isham, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/9/6/004 9, 1433 (1992), e-print arXiv:hep-th/9202053; A. Ashtekar and J. Lewandowski, J. Math. Phys. 0022-2488 10.1063/1.531037 36, 2170 (1995), e-print arXiv:gr-qc/9411046.
    • (1992) Class. Quantum Grav. , vol.9 , pp. 1433
    • Ashtekar, A.1    Isham, C.J.2    Ashtekar, A.3    Lewandowski, J.4
  • 5
    • 59349117516 scopus 로고    scopus 로고
    • Spectral analysis of the volume operator in loop quantum gravity
    • J. Math. Phys. 0022-2488 10.1063/1.532259, (), e-print arXiv:gr-qc/9606091;, Nucl. Phys. B 0550-3213 10.1016/S0550-3213(97)00334-9 500, 405 (1997), e-print arXiv:gr-qc/9706038;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/23/4/014 23, 1289 (2006), e-print arXiv:gr-qc/0405060;, "," e-print arXiv:gr-qc/0612147;, "," Class. Quantum Grav. 25, 065001 (2008);, " Properties of the volume operator in looquantum qravity. II. Detailed presentation," e-print arXiv:gq-qc/0706.0382.
    • T. Thiemann, J. Math. Phys. 0022-2488 10.1063/1.532259 39, 3347 (1998), e-print arXiv:gr-qc/9606091; R. Loll, Nucl. Phys. B 0550-3213 10.1016/S0550-3213(97)00334-9 500, 405 (1997), e-print arXiv:gr-qc/9706038; J. Brunnemann and T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/23/ 4/014 23, 1289 (2006), e-print arXiv:gr-qc/0405060; J. Brunnemann and D. Rideout, " Spectral analysis of the volume operator in loop quantum gravity.," e-print arXiv:gr-qc/0612147; J. Brunnemann and D. Rideout, " Properties of the volume operator in loop quantum gravity. I. Results.," Class. Quantum Grav. 25, 065001 (2008); J. Brunnemann and D. Rideout, " Properties of the volume operator in loop quantum qravity. II. Detailed presentation.," e-print arXiv:gq-qc/0706.0382.
    • (1998) Properties of the Volume Operator in Loop Quantum Gravity. I. Results , vol.39 , pp. 3347
    • Thiemann, T.1    Loll, R.2    Brunnemann, J.3    Thiemann, T.4    Brunnemann, J.5    Rideout, D.6    Brunnemann, J.7    Rideout, D.8    Brunnemann, J.9    Rideout, D.10
  • 6
    • 0242387526 scopus 로고    scopus 로고
    • Some comments on the representation theory of the algebra underlying loop quantum gravity
    • e-print arXiv:gr-qc/0207111;, "," e-print arXiv:gr-qc/0207112;, " On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories," e-print arXiv:gr-qc/0302090;, Commun. Math. Phys. 0010-3616 10.1007/s00220-008-0593-3, ();, " Representations of the Weyl algebra in quantum geometry," e-print arXiv:math-ph/0407006v2;, " Uniqueness of diffeomorphism invariant states on holonomy-flux algebras," Commun. Math. Phys. 267, 703 (2006).
    • H. Sahlmann, " Some comments on the representation theory of the algebra underlying loop quantum gravity.," e-print arXiv:gr-qc/0207111; H. Sahlmann, " When do measures on the space of connections support the triad operators of loop quantum gravity?," e-print arXiv:gr-qc/0207112; H. Sahlmann and T. Thiemann, " On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories.," e-print arXiv:gr-qc/0302090; H. Sahlmann and T. Thiemann, Commun. Math. Phys. 0010-3616 10.1007/s00220-008-0593-3 285, 67 (2009); C. Fleischhack, " Representations of the Weyl algebra in quantum geometry.," e-print arXiv:math-ph/ 0407006v2; J. Lewandowski, A. Okolow, H. Sahlmann, and T. Thiemann, " Uniqueness of diffeomorphism invariant states on holonomy-flux algebras.," Commun. Math. Phys. 267, 703 (2006).
    • (2009) When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity? , vol.285 , pp. 67
    • Sahlmann, H.1    Sahlmann, H.2    Sahlmann, H.3    Thiemann, T.4    Sahlmann, H.5    Thiemann, T.6    Fleischhack, C.7    Lewandowski, J.8    Okolow, A.9    Sahlmann, H.10    Thiemann, T.11
  • 7
    • 85045502395 scopus 로고    scopus 로고
    • e-print arXiv:gr-qc/9606088 0370-2693;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/4/011 15, 839 (1998), e-print arXiv:gr-qc/9606089;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/4/012 15, 875 (1998), e-print arXiv:gr-qc/9606090;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/010 15, 1207 (1998), e-print arXiv:gr-qc/9705017;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/011 15, 1249 (1998), e-print arXiv:gr-qc/9705018;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/012 15, 1281 (1998), e-print arXiv:gr-qc/9705019;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/6/005 15, 1463 (1998), e-print arXiv:gr-qc/9705020.
    • T. Thiemann, Phys. Lett. B 380, 257 (1996), e-print arXiv:gr-qc/9606088 0370-2693; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/4/ 011 15, 839 (1998), e-print arXiv:gr-qc/9606089; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/4/012 15, 875 (1998), e-print arXiv:gr-qc/9606090; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/010 15, 1207 (1998), e-print arXiv:gr-qc/9705017; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/011 15, 1249 (1998), e-print arXiv:gr-qc/9705018; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/5/012 15, 1281 (1998), e-print arXiv:gr-qc/9705019; T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/15/6/005 15, 1463 (1998), e-print arXiv:gr-qc/9705020.
    • (1996) Phys. Lett. B , vol.380 , pp. 257
    • Thiemann, T.1    Thiemann, T.2    Thiemann, T.3    Thiemann, T.4    Thiemann, T.5    Thiemann, T.6    Thiemann, T.7
  • 8
    • 35348954729 scopus 로고    scopus 로고
    • Partial and complete observables for Hamiltonian constrained systems
    • 0001-7701 10.1007/s10714-007-0495-2, ();, Gen. Relativ. Gravit. 0001-7701 23, 6155 (2006);, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/24/4/001 24, 757 (2007);, Class. Quantum Grav.; e-print arXiv:gr-qc/0702093.
    • B. Dittrich, " Partial and complete observables for Hamiltonian constrained systems.," Gen. Relativ. Gravit. 0001-7701 10.1007/s10714-007- 0495-2 39, 1891 (2007); B. Dittrich, Gen. Relativ. Gravit. 0001-7701 23, 6155 (2006); B. Dittrich, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/24/4/001 24, 757 (2007); B. Dittrich and J. Tambornino, Class. Quantum Grav.; B. Dittrich and J. Tambornino e-print arXiv:gr-qc/0702093.
    • (2007) Gen. Relativ. Gravit. , vol.39 , pp. 1891
    • Dittrich, B.1    Dittrich, B.2    Dittrich, B.3    Dittrich, B.4    Tambornino, J.5    Dittrich, B.6    Tambornino, J.7
  • 9
    • 32344436612 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/23/4/006, (), e-print arXiv:gr-qc/0411031.
    • T. Thiemann, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/23/4/006 23, 1163 (2006), e-print arXiv:gr-qc/0411031.
    • (2006) Class. Quantum Grav. , vol.23 , pp. 1163
    • Thiemann, T.1
  • 10
    • 33845343289 scopus 로고
    • Phys. Rev. D 0556-2821 10.1103/PhysRevD.43.442, ();, in, edited by A. Ashtekar and J. Stachel (Birkhäuser, Boston, 1991), 126;, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/8/2/011 8, 297 (1991);, Phys. Rev. D 0556-2821 10.1103/PhysRevD.65.124013 65, 124013 (2002), e-print arXiv:gr-qc/0110035.
    • C. Rovelli, Phys. Rev. D 0556-2821 10.1103/PhysRevD.43.442 43, 442 (1991); C. Rovelli, in Conceptional Problems in Quantum Gravity, edited by, A. Ashtekar, and, J. Stachel, (Birkhäuser, Boston, 1991), p. 126; C. Rovelli, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/8/2/011 8, 297 (1991); C. Rovelli, Phys. Rev. D 0556-2821 10.1103/PhysRevD.65.124013 65, 124013 (2002), e-print arXiv:gr-qc/0110035.
    • (1991) Conceptional Problems in Quantum Gravity , vol.43 , pp. 442
    • Rovelli, C.1    Rovelli, C.2    Rovelli, C.3    Rovelli, C.4
  • 11
    • 0037279440 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/20/8/304, (), e-print arXiv:gr-qc/0212077.
    • L. Freidel, E. R. Livine, and C. Rovelli, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/20/8/304 20, 1463 (2003), e-print arXiv:gr-qc/0212077.
    • (2003) Class. Quantum Grav. , vol.20 , pp. 1463
    • Freidel, L.1    Livine, E.R.2    Rovelli, C.3
  • 12
    • 27144553735 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/22/21/005, (), e-print arXiv:gr-qc/0402111.
    • K. Noui and A. Perez, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/ 22/21/005 22, 4489 (2005), e-print arXiv:gr-qc/0402111.
    • (2005) Class. Quantum Grav. , vol.22 , pp. 4489
    • Noui, K.1    Perez, A.2
  • 13
    • 24144441892 scopus 로고    scopus 로고
    • 0264-9381 10.1088/0264-9381/22/17/010, (), e-print arXiv:gr-qc/0501093.
    • S. Alexandrov and Z. Kadar, Class. Quantum Grav. 0264-9381 10.1088/0264-9381/22/17/010 22, 3491 (2005), e-print arXiv:gr-qc/0501093.
    • (2005) Class. Quantum Grav. , vol.22 , pp. 3491
    • Alexandrov, S.1    Kadar, Z.2
  • 14
    • 59349099692 scopus 로고
    • (North-Holland, Amsterdam), Vol..
    • A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1.
    • (1961) Quantum Mechanics , vol.1
    • Messiah, A.1
  • 15
    • 59349105019 scopus 로고    scopus 로고
    • When does a detector click?
    • e-print arXiv:quant-ph/0103144;, " Remarks on time-energy uncertainty relations," Rev. Math. Phys., (); e-print arXiv:quant-ph/ 0207048;, in, edited by V. K. Dobrev (Heron, Sofia, 2006).
    • R. Brunetti and K. Fredenhagen, " When does a detector click?," e-print arXiv:quant-ph/0103144; R. Brunetti and K. Fredenhagen, " Remarks on time-energy uncertainty relations.," Rev. Math. Phys. 14, 897 (2002); e-print arXiv:quant-ph/0207048; K. Fredenhagen, in Quantum Theory and Symmetries IV, edited by, V. K. Dobrev, (Heron, Sofia, 2006).
    • (2002) Quantum Theory and Symmetries IV , vol.14 , pp. 897
    • Brunetti, R.1    Fredenhagen, K.2    Brunetti, R.3    Fredenhagen, K.4    Fredenhagen, K.5
  • 16
    • 36749118349 scopus 로고
    • 0022-2488 10.1063/1.525745.
    • D. Basu and K. W. Wolf, J. Math. Phys. 0022-2488 10.1063/1.525745 24, 478 (1983).
    • (1983) J. Math. Phys. , vol.24 , pp. 478
    • Basu, D.1    Wolf, K.W.2
  • 17
    • 0034895143 scopus 로고    scopus 로고
    • 0556-2821 10.1103/PhysRevD.63.105014, (),e-print arXiv:gr-qc/0101057.
    • R. Gambini and R. A. Porto, Phys. Rev. D 0556-2821 10.1103/PhysRevD.63. 105014 63, 105014 (2001),e-print arXiv:gr-qc/0101057.
    • (2001) Phys. Rev. D , vol.63 , pp. 105014
    • Gambini, R.1    Porto, R.A.2

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