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Volumn 61, Issue 10, 2011, Pages 1881-1897

The spectral distance in the moyal plane

Author keywords

Compact quantum metric space; Moyal space; Noncommutative geometry; Spectral triple

Indexed keywords


EID: 79960378411     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2011.04.021     Document Type: Article
Times cited : (51)

References (44)
  • 2
    • 13644266460 scopus 로고    scopus 로고
    • On a classification of irreducible almost commutative geometries
    • Iochum B., Schücker T., Stephan C. On a classification of irreducible almost commutative geometries. J. Math. Phys. 2004, 45:5003-5041.
    • (2004) J. Math. Phys. , vol.45 , pp. 5003-5041
    • Iochum, B.1    Schücker, T.2    Stephan, C.3
  • 4
    • 0002152071 scopus 로고
    • Deformation quantization for actions of Rd
    • Rieffel M.A. Deformation quantization for actions of Rd. Mem. Amer. Math. Soc. 1993, 506.
    • (1993) Mem. Amer. Math. Soc. , vol.506
    • Rieffel, M.A.1
  • 5
    • 0000481618 scopus 로고
    • Quantum groups
    • Berkeley
    • Drinfeld V.G. Quantum groups. Proc. of the ICM 1986, vol. 1:798-820. Berkeley.
    • (1986) Proc. of the ICM , vol.1 , pp. 798-820
    • Drinfeld, V.G.1
  • 6
    • 0040323775 scopus 로고
    • A q-difference analogue of U(g) and the Yang-Baxter equation
    • Jimbo M. A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys. 1985, 10:63-69.
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63-69
    • Jimbo, M.1
  • 7
    • 0000595944 scopus 로고    scopus 로고
    • Noncommutative manifolds: the instanton algebra and isospectral deformations
    • Connes A., Landi G. Noncommutative manifolds: the instanton algebra and isospectral deformations. Comm. Math. Phys. 2001, 221:141-159.
    • (2001) Comm. Math. Phys. , vol.221 , pp. 141-159
    • Connes, A.1    Landi, G.2
  • 8
    • 0036026977 scopus 로고    scopus 로고
    • Noncommutative finite-dimensional manifolds I. Spherical manifolds and related examples
    • Connes A., Dubois-Violette M. Noncommutative finite-dimensional manifolds I. Spherical manifolds and related examples. Comm. Math. Phys. 2002, 230:539-579.
    • (2002) Comm. Math. Phys. , vol.230 , pp. 539-579
    • Connes, A.1    Dubois-Violette, M.2
  • 9
    • 0003277387 scopus 로고
    • The metric aspect of noncommutative geometry
    • Plenum, New York, New Symmetry Principles in Quantum Field Theory, Cargèse 1991
    • Connes A., Lott J. The metric aspect of noncommutative geometry. NATO Ad. Sci. Inst. Ser. B Phys. 1992, vol. 295:53-93. Plenum, New York.
    • (1992) NATO Ad. Sci. Inst. Ser. B Phys. , vol.295 , pp. 53-93
    • Connes, A.1    Lott, J.2
  • 10
    • 62549099628 scopus 로고    scopus 로고
    • On the spectral characterization of manifolds
    • [math.OA].
    • A. Connes, On the spectral characterization of manifolds, [math.OA]. arxiv:0810.2088.
    • Connes, A.1
  • 11
    • 84896062376 scopus 로고    scopus 로고
    • A view on optimal transport from noncommutative geometry
    • D'Andrea F., Martinetti P. A view on optimal transport from noncommutative geometry. SIGMA 2010, 6:057.
    • (2010) SIGMA , vol.6 , pp. 057
    • D'Andrea, F.1    Martinetti, P.2
  • 12
    • 0003051136 scopus 로고    scopus 로고
    • Distances in finite spaces from noncommutative geometry
    • Iochum B., Krajewski T., Martinetti P. Distances in finite spaces from noncommutative geometry. J. Geom. Phys. 2001, 37(1-2):100-125.
    • (2001) J. Geom. Phys. , vol.37 , Issue.1-2 , pp. 100-125
    • Iochum, B.1    Krajewski, T.2    Martinetti, P.3
  • 13
    • 0000533661 scopus 로고
    • Distances on a lattice from non-commutative geometry
    • Bimonte G., Lizzi F., Sparano G. Distances on a lattice from non-commutative geometry. Phys. Lett. 1994, B341:139-146.
    • (1994) Phys. Lett. , vol.B341 , pp. 139-146
    • Bimonte, G.1    Lizzi, F.2    Sparano, G.3
  • 14
    • 33745315388 scopus 로고    scopus 로고
    • Carnot-Carathéodory metric from gauge fluctuation in noncommutative geometry
    • Martinetti P. Carnot-Carathéodory metric from gauge fluctuation in noncommutative geometry. Comm. Math. Phys. 2006, 265:585-616.
    • (2006) Comm. Math. Phys. , vol.265 , pp. 585-616
    • Martinetti, P.1
  • 15
    • 0035981956 scopus 로고    scopus 로고
    • Discrete Kaluza Klein from scalar fluctuations in non-commutative geometry
    • Martinetti P., Wulkenhaar R. Discrete Kaluza Klein from scalar fluctuations in non-commutative geometry. J. Math. Phys. 2002, 43:182-204.
    • (2002) J. Math. Phys. , vol.43 , pp. 182-204
    • Martinetti, P.1    Wulkenhaar, R.2
  • 16
    • 50649122514 scopus 로고    scopus 로고
    • Spectral distance on the circle
    • Martinetti P. Spectral distance on the circle. J. Funct. Anal. 2008, 255:1575-1612.
    • (2008) J. Funct. Anal. , vol.255 , pp. 1575-1612
    • Martinetti, P.1
  • 18
    • 34547163935 scopus 로고    scopus 로고
    • Bounded-Lipschitz distances on the state space of a C*-algebra
    • Latrémolière F. Bounded-Lipschitz distances on the state space of a C*-algebra. Taiwanese J. Math. 2007, 11(2):447-469.
    • (2007) Taiwanese J. Math. , vol.11 , Issue.2 , pp. 447-469
    • Latrémolière, F.1
  • 19
    • 79960346815 scopus 로고    scopus 로고
    • Dynamical systems on spectral metric spaces, [math.OA].
    • J.V. Bellissard, M. Marcolli, K. Reihani, Dynamical systems on spectral metric spaces, 2010, [math.OA]. arxiv:1008.4617.
    • (2010)
    • Bellissard, J.V.1    Marcolli, M.2    Reihani, K.3
  • 20
    • 0000176173 scopus 로고    scopus 로고
    • Metric on state spaces
    • Rieffel M.A. Metric on state spaces. Doc. Math. 1999, 4:559-600.
    • (1999) Doc. Math. , vol.4 , pp. 559-600
    • Rieffel, M.A.1
  • 21
    • 30444446364 scopus 로고    scopus 로고
    • Compact quantum metric spaces
    • AMS, Providence, RI, Operator Algebras, Quantization, and Noncommutative Geometry
    • Rieffel M.A. Compact quantum metric spaces. Contemp. Math. 2004, vol. 365:315-330. AMS, Providence, RI.
    • (2004) Contemp. Math. , vol.365 , pp. 315-330
    • Rieffel, M.A.1
  • 22
    • 36549090874 scopus 로고
    • Algebras of distributions suitable for phase-space quantum mechanics. I
    • Gracia-Bondía J.M., Várilly J.C. Algebras of distributions suitable for phase-space quantum mechanics. I. J. Math. Phys. 1988, 29(4):869-879.
    • (1988) J. Math. Phys. , vol.29 , Issue.4 , pp. 869-879
    • Gracia-Bondía, J.M.1    Várilly, J.C.2
  • 23
    • 36549100229 scopus 로고
    • Algebras of distributions suitable for phase-space quantum mechanics. II
    • Gracia-Bondía J.M., Várilly J.C. Algebras of distributions suitable for phase-space quantum mechanics. II. J. Math. Phys. 1988, 29(4):880-887.
    • (1988) J. Math. Phys. , vol.29 , Issue.4 , pp. 880-887
    • Gracia-Bondía, J.M.1    Várilly, J.C.2
  • 24
    • 17444364853 scopus 로고    scopus 로고
    • The spectral action for Moyal planes
    • Gayral V., Iochum B. The spectral action for Moyal planes. J. Math. Phys. 2005, 46:043503.
    • (2005) J. Math. Phys. , vol.46 , pp. 043503
    • Gayral, V.1    Iochum, B.2
  • 25
    • 78650903525 scopus 로고    scopus 로고
    • Noncommutative Yang-Mills-Higgs actions from derivation based differential calculus
    • Cagnache E., Masson T., Wallet J.C. Noncommutative Yang-Mills-Higgs actions from derivation based differential calculus. J. Noncommut. Geom. 2011, 5:39-67.
    • (2011) J. Noncommut. Geom. , vol.5 , pp. 39-67
    • Cagnache, E.1    Masson, T.2    Wallet, J.C.3
  • 26
    • 77954206253 scopus 로고    scopus 로고
    • Derivations of the Moyal algebra and noncommutative gauge theories
    • Wallet J.C. Derivations of the Moyal algebra and noncommutative gauge theories. SIGMA 2009, 5:013.
    • (2009) SIGMA , vol.5 , pp. 013
    • Wallet, J.C.1
  • 28
    • 84952911698 scopus 로고
    • Quantum mechanics as a statistical theory
    • Moyal J.E. Quantum mechanics as a statistical theory. Proc. Cambridge Philos. Soc. 1949, 45:99-124.
    • (1949) Proc. Cambridge Philos. Soc. , vol.45 , pp. 99-124
    • Moyal, J.E.1
  • 29
    • 33745040449 scopus 로고
    • On the principles of elementary quantum mechanics
    • Groenewold H.J. On the principles of elementary quantum mechanics. Physica 1946, 12:405-460.
    • (1946) Physica , vol.12 , pp. 405-460
    • Groenewold, H.J.1
  • 30
    • 78649692983 scopus 로고    scopus 로고
    • Quantum geometry on quantum spacetime: distance, area and volume operators
    • [hep-th].
    • D. Bahns, S. Doplicher, K. Fredenhagen, G. Piacitelli, Quantum geometry on quantum spacetime: distance, area and volume operators, [hep-th]. arxiv:1005.2130.
    • Bahns, D.1    Doplicher, S.2    Fredenhagen, K.3    Piacitelli, G.4
  • 31
  • 32
    • 79960348928 scopus 로고    scopus 로고
    • Minimal length in quantum space and integration of the line element in noncommutative geometry
    • preprint, .
    • P. Martinetti, F. Mercati, L. Tomasini, Minimal length in quantum space and integration of the line element in noncommutative geometry, preprint, arxiv:1106.0261.
    • Martinetti, P.1    Mercati, F.2    Tomasini, L.3
  • 33
    • 17744376433 scopus 로고    scopus 로고
    • Renormalisation of φ4-theory on noncommutative R4 in the matrix base
    • Grosse H., Wulkenhaar R. Renormalisation of φ4-theory on noncommutative R4 in the matrix base. Comm. Math. Phys. 2005, 256:305-374.
    • (2005) Comm. Math. Phys. , vol.256 , pp. 305-374
    • Grosse, H.1    Wulkenhaar, R.2
  • 34
    • 31744433769 scopus 로고    scopus 로고
    • Renormalization of noncommutative phi 4-theory by multi-scale analysis
    • Rivasseau V., Vignes-Tourneret F., Wulkenhaar R. Renormalization of noncommutative phi 4-theory by multi-scale analysis. Comm. Math. Phys. 2006, 262:565-594.
    • (2006) Comm. Math. Phys. , vol.262 , pp. 565-594
    • Rivasseau, V.1    Vignes-Tourneret, F.2    Wulkenhaar, R.3
  • 35
    • 21844496057 scopus 로고
    • Noncommutative geometry and reality
    • Connes A. Noncommutative geometry and reality. J. Math. Phys. 1995, 36:6194-6231.
    • (1995) J. Math. Phys. , vol.36 , pp. 6194-6231
    • Connes, A.1
  • 36
    • 67650538964 scopus 로고    scopus 로고
    • Complete positivity of Rieffel's deformation quantization by actions of Rd
    • Kaschek D., Neumaier N., Waldmann S. Complete positivity of Rieffel's deformation quantization by actions of Rd. J. Noncommut. Geom. 2009, 3:361-375.
    • (2009) J. Noncommut. Geom. , vol.3 , pp. 361-375
    • Kaschek, D.1    Neumaier, N.2    Waldmann, S.3
  • 37
    • 35348966113 scopus 로고    scopus 로고
    • Operator algebras. Theory of C*-algebras and von Neumann algebras
    • Blackadar B. Operator algebras. Theory of C*-algebras and von Neumann algebras. Encyclopaedia Math. Sci. 2006, 122.
    • (2006) Encyclopaedia Math. Sci. , vol.122
    • Blackadar, B.1
  • 39
    • 1342305282 scopus 로고    scopus 로고
    • Gromov-Hausdorff distance for quantum metric spaces. Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
    • Rieffel M.A. Gromov-Hausdorff distance for quantum metric spaces. Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance. Mem. Amer. Math. Soc. 2004, 168(796):1-65.
    • (2004) Mem. Amer. Math. Soc. , vol.168 , Issue.796 , pp. 1-65
    • Rieffel, M.A.1
  • 43
    • 0003249219 scopus 로고
    • A representation theory for commutative topological algebra
    • Kadison R.V. A representation theory for commutative topological algebra. Mem. Amer. Math. Soc. 1951, 7.
    • (1951) Mem. Amer. Math. Soc. , vol.7
    • Kadison, R.V.1
  • 44
    • 33750394813 scopus 로고    scopus 로고
    • Spectral triples for AF C*-algebras and metrics on the Cantor set
    • Christensen E., Ivan C. Spectral triples for AF C*-algebras and metrics on the Cantor set. J. Oper. Theory 2006, 56:1:17-46.
    • (2006) J. Oper. Theory , pp. 17-46
    • Christensen, E.1    Ivan, C.2


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