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Volumn 41, Issue 6, 2000, Pages 3832-3866

A short survey of noncommutative geometry

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EID: 0034395487     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533329     Document Type: Review
Times cited : (135)

References (88)
  • 1
    • 0001380544 scopus 로고
    • Une classification des facteurs de type III
    • A. Connes, "Une classification des facteurs de type III," Ann. Sci. Ecole Norm. Sup. 6(4), 133-252 (1973).
    • (1973) Ann. Sci. Ecole Norm. Sup. , vol.6 , Issue.4 , pp. 133-252
    • Connes, A.1
  • 2
    • 0002260681 scopus 로고
    • Tomita's theory of modular Hilbert algebras and its applications
    • Springer, New York
    • M. Takesaki, Tomita's theory of modular Hilbert algebras and its applications, in Lecture Notes in Mathematics, Vol. 128 (Springer, New York, 1970).
    • (1970) Lecture Notes in Mathematics , vol.128
    • Takesaki, M.1
  • 3
    • 0000389660 scopus 로고
    • Duality for crossed products and the structure of von Neumann algebras of type III
    • M. Takesaki, "Duality for crossed products and the structure of von Neumann algebras of type III," Acta Math. 131, 249-310 (1973).
    • (1973) Acta Math. , vol.131 , pp. 249-310
    • Takesaki, M.1
  • 4
    • 0002562118 scopus 로고
    • On ergodic flows and the isomorphism of factors
    • W. Krieger, "On ergodic flows and the isomorphism of factors," Math. Ann. 223, 19-70 (1976).
    • (1976) Math. Ann. , vol.223 , pp. 19-70
    • Krieger, W.1
  • 5
    • 84972556832 scopus 로고
    • The flow of weights on factors of type III
    • A. Connes and M. Takesaki, "The flow of weights on factors of type III," Tohoku Math. J. 29, 473-575 (1977).
    • (1977) Tohoku Math. J. , vol.29 , pp. 473-575
    • Connes, A.1    Takesaki, M.2
  • 6
    • 0002179940 scopus 로고
    • Classification of injective factors
    • A. Connes, "Classification of injective factors," Ann. Math. 104(2), 73-115 (1976).
    • (1976) Ann. Math. , vol.104 , Issue.2 , pp. 73-115
    • Connes, A.1
  • 7
    • 0001523467 scopus 로고
    • Outer conjugacy classes of automorphisms of factors
    • A. Connes, "Outer conjugacy classes of automorphisms of factors," Ann. Sci. Ecole Norm. Sup. 8(4), 383-419 (1975).
    • (1975) Ann. Sci. Ecole Norm. Sup. , vol.8 , Issue.4 , pp. 383-419
    • Connes, A.1
  • 8
    • 0007386136 scopus 로고
    • λ and closure of inner automorphisms
    • λ and closure of inner automorphisms," J. Operator Theory 14, 189-211 (1985).
    • (1985) J. Operator Theory , vol.14 , pp. 189-211
    • Connes, A.1
  • 12
    • 0039417176 scopus 로고
    • Future extensions of index theory and elliptic operators
    • I. M. Singer, "Future extensions of index theory and elliptic operators," Ann. Math. Studies 70, 171-185 (1971).
    • (1971) Ann. Math. Studies , vol.70 , pp. 171-185
    • Singer, I.M.1
  • 13
    • 0001109595 scopus 로고
    • Extensions of C*-algebras and K-homology
    • L. G. Brown, R. G. Douglas, and P. A. Fillmore, "Extensions of C*-algebras and K-homology," Ann. Math. 105, 265-324 (1977).
    • (1977) Ann. Math. , vol.105 , pp. 265-324
    • Brown, L.G.1    Douglas, R.G.2    Fillmore, P.A.3
  • 14
    • 24444478704 scopus 로고    scopus 로고
    • C* algebras and K theory
    • Algebraic Topology, Aarhus 1978. Springer-Verlag
    • A. S. Miscenko, "C* algebras and K theory," in Algebraic Topology, Aarhus 1978. Lecture Notes in Mathematics Vol. 763 (Springer-Verlag, Vol. 1979), pp. 262-274.
    • Lecture Notes in Mathematics , vol.763-1979 , pp. 262-274
    • Miscenko, A.S.1
  • 15
    • 0001170704 scopus 로고
    • The operator K-functor and extensions of C* algebras
    • G. G. Kasparov, "The operator K-functor and extensions of C* algebras," Izv. Akad. Nauk SSSR, Ser. Mat. 44, 571-636 (1980), Math. USSR Izv. 16, 513-572 (1981).
    • (1980) Izv. Akad. Nauk SSSR, Ser. Mat. , vol.44 , pp. 571-636
    • Kasparov, G.G.1
  • 16
    • 0001241676 scopus 로고
    • G. G. Kasparov, "The operator K-functor and extensions of C* algebras," Izv. Akad. Nauk SSSR, Ser. Mat. 44, 571-636 (1980), Math. USSR Izv. 16, 513-572 (1981).
    • (1981) Math. USSR Izv. , vol.16 , pp. 513-572
  • 17
    • 0002490022 scopus 로고
    • Geometric K-theory for Lie groups and foliations
    • Preprint IHES (M/82/)
    • P. Baum and A. Connes, "Geometric K-theory for Lie groups and foliations," Preprint IHES (M/82/), 1982, to appear in l'Enseignement Mathematique 46, 1-35 (2000).
    • (1982) L'Enseignement Mathematique , vol.46 , pp. 1-35
    • Baum, P.1    Connes, A.2
  • 18
    • 0002739380 scopus 로고
    • A geometric construction of the discrete series for semisimple Lie groups
    • M. F. Atiyah and W. Schmid, "A geometric construction of the discrete series for semisimple Lie groups," Invent. Math. 42, 1-62 (1977).
    • (1977) Invent. Math. , vol.42 , pp. 1-62
    • Atiyah, M.F.1    Schmid, W.2
  • 19
    • 24444444258 scopus 로고
    • Approche de la conjecture de Novikov par la cohomologie cyclique
    • G. Skandalis, "Approche de la conjecture de Novikov par la cohomologie cyclique," Seminaire Bourbaki, (1990-91), Expose 739 201-202-203, 299-316 (1992).
    • (1992) Seminaire Bourbaki, (1990-91), Expose 739 , vol.201-203 , pp. 299-316
    • Skandalis, G.1
  • 20
    • 33747402355 scopus 로고    scopus 로고
    • Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes
    • P. Julg, "Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes," Seminaire Bourbaki, (1997-98), Expose 841 252, 151-183 (1998).
    • (1998) Seminaire Bourbaki, (1997-98), Expose 841 , vol.252 , pp. 151-183
    • Julg, P.1
  • 21
    • 85037765135 scopus 로고    scopus 로고
    • Progres recents sur la conjecture de Baum-Connes, contribution de Vincent Lafforgue
    • G. Skandalis, "Progres recents sur la conjecture de Baum-Connes, contribution de Vincent Lafforgue," Seminaire Bourbaki (1999-2000), Expose 869.
    • Seminaire Bourbaki (1999-2000), Expose 869
    • Skandalis, G.1
  • 23
    • 29944446209 scopus 로고    scopus 로고
    • Spectral sequence and homology of currents for operator algebras
    • 41/81
    • A. Connes, "Spectral sequence and homology of currents for operator algebras," Math. Forschungsinst. Oberwolfach Tagungsber., 41/81; Funktionalanalysis und C*-Algebren, 27-9/3-10 (1981).
    • Math. Forschungsinst. Oberwolfach Tagungsber.
    • Connes, A.1
  • 24
    • 0040009362 scopus 로고
    • 279/310
    • A. Connes, "Spectral sequence and homology of currents for operator algebras," Math. Forschungsinst. Oberwolfach Tagungsber., 41/81; Funktionalanalysis und C*-Algebren, 27-9/3-10 (1981).
    • (1981) Funktionalanalysis und C*-Algebren
  • 26
    • 0040602666 scopus 로고
    • Preprint IHES (M/83/19)
    • A. Connes, "Noncommutative differential geometry. Part I: The Chern character in K-homology," Preprint IHES (M/82/53) (1982); Part II: de Rham homology and noncommutative algebra, Preprint IHES (M/83/19) (1983).
    • (1983) Part II: De Rham Homology and Noncommutative Algebra
  • 28
    • 0000089675 scopus 로고
    • Homology of matrix Lie algebras over rings and the Hochschild homology
    • B. L. Tsygan, "Homology of matrix Lie algebras over rings and the Hochschild homology," Usp. Mat. Nauk 38, 217-218 (1983).
    • (1983) Usp. Mat. Nauk , vol.38 , pp. 217-218
    • Tsygan, B.L.1
  • 29
    • 0000923270 scopus 로고
    • Cyclic cohomology, the Novikov conjecture and hyperbolic groups
    • A. Connes and H. Moscovici, "Cyclic cohomology, the Novikov conjecture and hyperbolic groups," Topology 29, 345-388 (1990).
    • (1990) Topology , vol.29 , pp. 345-388
    • Connes, A.1    Moscovici, H.2
  • 30
    • 0002546810 scopus 로고
    • "Cyclic cohomology and the transverse fundamental class of a foliation," Geometric methods in operator algebras
    • Kyoto, Longman, Harlow
    • A. Connes, "Cyclic cohomology and the transverse fundamental class of a foliation," Geometric methods in operator algebras (Kyoto, 1983), Pitman Research Notes in Mathematics Vol. 123 (Longman, Harlow, 1986), pp. 52-144.
    • (1983) Pitman Research Notes in Mathematics , vol.123 , pp. 52-144
    • Connes, A.1
  • 32
    • 51249178483 scopus 로고
    • The cyclic homology of the group rings
    • D. Burghelea, "The cyclic homology of the group rings," Comment. Math. Helv. 60, 354-365 (1985).
    • (1985) Comment. Math. Helv. , vol.60 , pp. 354-365
    • Burghelea, D.1
  • 33
    • 84967713498 scopus 로고
    • Cyclic homology and singularity
    • J. Cuntz and D. Quillen, "Cyclic homology and singularity," J. Am. Math. Soc. 8, 373-442 (1995).
    • (1995) J. Am. Math. Soc. , vol.8 , pp. 373-442
    • Cuntz, J.1    Quillen, D.2
  • 34
    • 85029961314 scopus 로고    scopus 로고
    • Operators on noncommutative differential forms and cyclic homology
    • to appear
    • J. Cuntz, and D. Quillen, "Operators on noncommutative differential forms and cyclic homology," J. Differential Geometry, to appear.
    • J. Differential Geometry
    • Cuntz, J.1    Quillen, D.2
  • 35
    • 0011587326 scopus 로고
    • On excision in periodic cyclic cohomology, I and II
    • J. Cuntz and D. Quillen, "On excision in periodic cyclic cohomology, I and II," C. R. Acad. Sci. Paris, Ser. I Math. 317, 917-922 (1993); 318, 11-12 (1994).
    • (1993) C. R. Acad. Sci. Paris, Ser. I Math. , vol.317 , pp. 917-922
    • Cuntz, J.1    Quillen, D.2
  • 36
    • 0041196683 scopus 로고
    • J. Cuntz and D. Quillen, "On excision in periodic cyclic cohomology, I and II," C. R. Acad. Sci. Paris, Ser. I Math. 317, 917-922 (1993); 318, 11-12 (1994).
    • (1994) C. R. Acad. Sci. Paris, Ser. I Math. , vol.318 , pp. 11-12
  • 37
    • 0003193329 scopus 로고    scopus 로고
    • Operads and motives in deformation quantization
    • M. Kontsevich, "Operads and motives in Deformation Quantization," Lett. Math. Phys. 48(1), 35-72 (1999).
    • (1999) Lett. Math. Phys. , vol.48 , Issue.1 , pp. 35-72
    • Kontsevich, M.1
  • 41
    • 0002326199 scopus 로고
    • Noncommutative residue, part I. Fundamentals K-theory, arithmetic and geometry
    • Springer, Berlin
    • M. Wodzicki, "Noncommutative residue, Part I. Fundamentals K-theory, arithmetic and geometry," Lecture Notes in Mathematics Vol. 1289 (Springer, Berlin, 1987).
    • (1987) Lecture Notes in Mathematics , vol.1289
    • Wodzicki, M.1
  • 42
  • 43
    • 0010782941 scopus 로고
    • Geometric periodicity and the invariants of manifolds
    • Springer, New York
    • D. Sullivan, "Geometric periodicity and the invariants of manifolds," Lecture Notes in Mathematics Vol. 197 (Springer, New York, 1971).
    • (1971) Lecture Notes in Mathematics , vol.197
    • Sullivan, D.1
  • 45
    • 51249175185 scopus 로고
    • Entire cyclic cohomology of Banach algebras and characters of θ summable Fredholm modules
    • A. Connes, "Entire cyclic cohomology of Banach algebras and characters of θ summable Fredholm modules," K-theory 1, 519-548 (1988).
    • (1988) K-theory , vol.1 , pp. 519-548
    • Connes, A.1
  • 47
    • 0000151581 scopus 로고
    • The local index formula in noncommutative geometry
    • A. Connes and H. Moscovici, "The local index formula in noncommutative geometry," GAFA 5, 174-243 (1995).
    • (1995) GAFA , vol.5 , pp. 174-243
    • Connes, A.1    Moscovici, H.2
  • 49
    • 0032210257 scopus 로고    scopus 로고
    • Hopf algebras, cyclic cohomology and the transverse index theorem
    • A. Connes and H. Moscovici, "Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem," Commun. Math. Phys. 198, 199-246 (1998).
    • (1998) Commun. Math. Phys. , vol.198 , pp. 199-246
    • Connes, A.1    Moscovici, H.2
  • 50
    • 0003177050 scopus 로고
    • Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov
    • M. Hilsum and G. Skandalis, "Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov," Ann. Sci. Ecole Norm. Sup. 20(4), 325-390 (1987).
    • (1987) Ann. Sci. Ecole Norm. Sup. , vol.20 , Issue.4 , pp. 325-390
    • Hilsum, M.1    Skandalis, G.2
  • 52
  • 53
    • 0003046491 scopus 로고    scopus 로고
    • Cyclic cohomology and Hopf algebras
    • A. Connes and H. Moscovici, "Cyclic Cohomology and Hopf Algebras," Lett. Math. Phys. 48(1), 97-108 (1999).
    • (1999) Lett. Math. Phys. , vol.48 , Issue.1 , pp. 97-108
    • Connes, A.1    Moscovici, H.2
  • 54
    • 0001330424 scopus 로고    scopus 로고
    • Renormalization automated by Hopf algebras
    • hep-th/9810087
    • D. J. Broadhurst and D. Kreimer, "Renormalization automated by Hopf algebras," J. Symb. Comput. 27, 581 (1999); hep-th/9810087: D. Kreimer and R. Delbourgo, "Using the Hopf algebra structure of Quantum Field Theory in calculations," Phys. Rev. D 60, 105025 (1999); hep-th/9903249.
    • (1999) J. Symb. Comput. , vol.27 , pp. 581
    • Broadhurst, D.J.1    Kreimer, D.2
  • 55
    • 18144402422 scopus 로고    scopus 로고
    • Using the Hopf algebra structure of quantum field theory in calculations
    • hep-th/9903249
    • D. J. Broadhurst and D. Kreimer, "Renormalization automated by Hopf algebras," J. Symb. Comput. 27, 581 (1999); hep-th/9810087: D. Kreimer and R. Delbourgo, "Using the Hopf algebra structure of Quantum Field Theory in calculations," Phys. Rev. D 60, 105025 (1999); hep-th/9903249.
    • (1999) Phys. Rev. D , vol.60 , pp. 105025
    • Kreimer, D.1    Delbourgo, R.2
  • 56
    • 0001350459 scopus 로고    scopus 로고
    • The four-loop beta-function in quantum chromodynamics
    • T. van Ritbergen, J. A. M. Vermaseren, and S. A. Larin, "The four-loop beta-function in Quantum Chromodynamics," Phys. Lett. B 400, 379-384 (1997).
    • (1997) Phys. Lett. B , vol.400 , pp. 379-384
    • Van Ritbergen, T.1    Vermaseren, J.A.M.2    Larin, S.A.3
  • 57
    • 33646035766 scopus 로고    scopus 로고
    • On the Hopf algebra structure of perturbative quantum field theory
    • 2.2, q-alg/9707029
    • D. Kreimer, "On the Hopf algebra structure of perturbative Quantum Field Theory," Adv. Theor. Math. Phys. 2.2, 303 (1998); q-alg/9707029.
    • (1998) Adv. Theor. Math. Phys. , pp. 303
    • Kreimer, D.1
  • 58
    • 0033426909 scopus 로고    scopus 로고
    • On overlapping divergencies
    • hep-th/9810022
    • D. Kreimer, "On overlapping divergencies," Commun. Math. Phys. 204, 669 (1999); hep-th/9810022.
    • (1999) Commun. Math. Phys. , vol.204 , pp. 669
    • Kreimer, D.1
  • 59
    • 33748744827 scopus 로고    scopus 로고
    • Chen's iterated integral represents the operator product expansion
    • 3.3 hep-th/9901099
    • D. Kreimer, "Chen's iterated integral represents the operator product expansion," Adv. Theor. Math. Phys. 3.3 (1999); hep-th/9901099; D. Kreimer and R. Delbourgo, "Using the Hopf algebra structure of Quantum Field Theory in calculations," Phys. Rev. D 60, 105025 (1999); hep-th/9903249.
    • (1999) Adv. Theor. Math. Phys.
    • Kreimer, D.1
  • 60
    • 18144402422 scopus 로고    scopus 로고
    • Using the Hopf algebra structure of quantum field theory in calculations
    • hep-th/9903249
    • D. Kreimer, "Chen's iterated integral represents the operator product expansion," Adv. Theor. Math. Phys. 3.3 (1999); hep-th/9901099; D. Kreimer and R. Delbourgo, "Using the Hopf algebra structure of Quantum Field Theory in calculations," Phys. Rev. D 60, 105025 (1999); hep-th/9903249.
    • (1999) Phys. Rev. D , vol.60 , pp. 105025
    • Kreimer, D.1    Delbourgo, R.2
  • 61
    • 0032257297 scopus 로고    scopus 로고
    • Hopf algebras, renormalization and noncommutative geometry
    • hep-th/9808042
    • A. Connes and D. Kreimer, "Hopf algebras, Renormalization and Noncommutative Geometry," Commun. Math. Phys. 199, 203 (1998); hep-th/9808042.
    • (1998) Commun. Math. Phys. , vol.199 , pp. 203
    • Connes, A.1    Kreimer, D.2
  • 62
    • 33646057705 scopus 로고    scopus 로고
    • Renormalization in quantum field theory and the Riemann-Hilbert problem
    • hep-th/9909126
    • A. Connes and D. Kreimer, "Renormalization in quantum field theory and the Riemann-Hilbert problem," J. High Energy Phys. 09, 024 (1999); hep-th/9909126.
    • (1999) J. High Energy Phys. , vol.9 , pp. 024
    • Connes, A.1    Kreimer, D.2
  • 63
    • 85037752655 scopus 로고    scopus 로고
    • Renormalization in quantum field theory and the Riemann-Hilbert problem I: The Hopf algebra structure of graphs and the main theorem
    • hep-th/9912092
    • A. Connes and D. Kreimer, "Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem." To appear in Commun. Math. Phys.; hep-th/9912092.
    • Commun. Math. Phys.
    • Connes, A.1    Kreimer, D.2
  • 64
    • 0030359659 scopus 로고    scopus 로고
    • Gravity coupled with matter and foundation of noncommutative geometry
    • A. Connes, "Gravity coupled with matter and foundation of noncommutative geometry," Commun. Math. Phys. 182, 155-176 (1996).
    • (1996) Commun. Math. Phys. , vol.182 , pp. 155-176
    • Connes, A.1
  • 65
    • 0001433377 scopus 로고
    • Gravity, noncommutative geometry and the Wodzicki residue
    • W. Kalau and M. Walze, "Gravity, noncommutative geometry and the Wodzicki residue," J. Geom. Phys. 16, 327-344 (1995).
    • (1995) J. Geom. Phys. , vol.16 , pp. 327-344
    • Kalau, W.1    Walze, M.2
  • 66
    • 0001284725 scopus 로고
    • The Dirac operator and gravitation
    • D. Kastler, "The Dirac operator and gravitation," Commun. Math. Phys. 166, 633-643 (1995).
    • (1995) Commun. Math. Phys. , vol.166 , pp. 633-643
    • Kastler, D.1
  • 67
    • 21844496057 scopus 로고
    • Noncommutative geometry and reality
    • A. Connes, "Noncommutative geometry and reality," J. Math. Phys. 36, 6194-6231 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 6194-6231
    • Connes, A.1
  • 69
    • 0002200267 scopus 로고
    • Morita equivalence for C*-algebras and W*-algebras
    • M. A. Rieffel, "Morita equivalence for C*-algebras and W*-algebras," J. Pure Appl. Algebra 5, 51-96 (1974).
    • (1974) J. Pure Appl. Algebra , vol.5 , pp. 51-96
    • Rieffel, M.A.1
  • 71
    • 4244084091 scopus 로고    scopus 로고
    • Universal formulas for noncommutative geometry actions
    • A. Chamseddine and A. Connes, "Universal formulas for noncommutative geometry actions," Phys. Rev. Lett. 77(24), 4868-4871 (1996).
    • (1996) Phys. Rev. Lett. , vol.77 , Issue.24 , pp. 4868-4871
    • Chamseddine, A.1    Connes, A.2
  • 73
    • 0039659940 scopus 로고
    • Quasihomomorphismes, cohomologie cyclique et positivite
    • A. Connes and J. Cuntz, "Quasihomomorphismes, cohomologie cyclique et positivite," Commun. Math. Phys. 114, 515-526 (1988).
    • (1988) Commun. Math. Phys. , vol.114 , pp. 515-526
    • Connes, A.1    Cuntz, J.2
  • 74
    • 84972491035 scopus 로고
    • C*-algebras associated with irrational rotations
    • M. A. Rieffel, "C*-algebras associated with irrational rotations," Pac. J. Math. 93, 415-429 (1981).
    • (1981) Pac. J. Math. , vol.93 , pp. 415-429
    • Rieffel, M.A.1
  • 75
    • 0002819043 scopus 로고
    • Exact sequences for K groups and Ext group of certain crossed product C*-algebras
    • M. Pimsner and D. Voiculescu, "Exact sequences for K groups and Ext group of certain crossed product C*-algebras," J. Operator Theory 4, 93-118 (1980).
    • (1980) J. Operator Theory , vol.4 , pp. 93-118
    • Pimsner, M.1    Voiculescu, D.2
  • 76
    • 84959829172 scopus 로고
    • The cancellation theorem for projective modules over irrational rotation C*-algebras
    • M. A. Rieffel, "The cancellation theorem for projective modules over irrational rotation C*-algebras," Proc. London Math. Soc. 47, 285-302 (1983).
    • (1983) Proc. London Math. Soc. , vol.47 , pp. 285-302
    • Rieffel, M.A.1
  • 77
    • 0001534815 scopus 로고
    • Yang-Mills for noncummutative two tori
    • Iowa City, Iowa
    • A. Connes and M. Rieffel, "Yang-Mills for noncummutative two tori," in Operator Algebras and Mathematical Physics (Iowa City, Iowa, 1985), pp. 237-266; Contemp. Math. Oper. Algebra Math. Phys. Vol. 62: (American Mathematical Society, Providence, RI, 1987).
    • (1985) Operator Algebras and Mathematical Physics , pp. 237-266
    • Connes, A.1    Rieffel, M.2
  • 78
    • 0004037801 scopus 로고
    • American Mathematical Society, Providence, RI
    • A. Connes and M. Rieffel, "Yang-Mills for noncummutative two tori," in Operator Algebras and Mathematical Physics (Iowa City, Iowa, 1985), pp. 237-266; Contemp. Math. Oper. Algebra Math. Phys. Vol. 62: (American Mathematical Society, Providence, RI, 1987).
    • (1987) Contemp. Math. Oper. Algebra Math. Phys. , vol.62
  • 79
    • 0041524804 scopus 로고    scopus 로고
    • Noncommutative geometry and Matrix theory: Compactification on tori
    • A. Connes, M. Douglas, and A. Schwarz, "Noncommutative geometry and Matrix theory: compactification on tori," J. High Energy Physics 2 (1998).
    • (1998) J. High Energy Physics , vol.2
    • Connes, A.1    Douglas, M.2    Schwarz, A.3
  • 81
  • 82
    • 4243473139 scopus 로고    scopus 로고
    • Divergences in a field theory on a quantum space
    • T. Filk, "Divergences in a field theory on a quantum space," Phys. Lett. B 376, 53-58 (1996).
    • (1996) Phys. Lett. B , vol.376 , pp. 53-58
    • Filk, T.1
  • 86
    • 0000907877 scopus 로고    scopus 로고
    • On the ultraviolet behaviour of quantum fields over noncommutative manifolds
    • J. C. Varilly and J. M. Gracia-Bondia, "On the ultraviolet behaviour of quantum fields over noncommutative manifolds," Int. J. Mod. Phys. A 14, 1305-1323 (1999).
    • (1999) Int. J. Mod. Phys. A , vol.14 , pp. 1305-1323
    • Varilly, J.C.1    Gracia-Bondia, J.M.2
  • 87
    • 0002840475 scopus 로고
    • Essay on physics and noncommutative geometry
    • Oxford U.P., New York
    • A. Connes, "Essay on physics and noncommutative geometry," in The Interface of Mathematics and Particle Physics, (Oxford U.P., New York, 1990), pp. 9-48.
    • (1990) The Interface of Mathematics and Particle Physics , pp. 9-48
    • Connes, A.1


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