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Volumn 12, Issue 1, 2000, Pages 91-137

Cover of the Brownian bridge and stochastic symplectic action

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EID: 0040016391     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X00000058     Document Type: Article
Times cited : (22)

References (88)
  • 1
    • 0001696024 scopus 로고
    • On the cobar construction
    • J. F. Adams, "On the cobar construction", Proc. Natl. Acad. Sci. USA 42 (1956) 346-373.
    • (1956) Proc. Natl. Acad. Sci. USA , vol.42 , pp. 346-373
    • Adams, J.F.1
  • 2
    • 44049116976 scopus 로고
    • A general class of infinite dimensional operators and path representation of their index
    • A. Arai, "A general class of infinite dimensional operators and path representation of their index", J.F.A. 105 (1992) 342-408.
    • (1992) J.F.A. , vol.105 , pp. 342-408
    • Arai, A.1
  • 3
    • 0002298999 scopus 로고
    • De Rham-Hodge-Kodaira decomposition in infinite dimension
    • A. Arai and I. Mitoma, "De Rham-Hodge-Kodaira decomposition in infinite dimension", Math. Ann. 291 (1991) 51-73.
    • (1991) Math. Ann. , vol.291 , pp. 51-73
    • Arai, A.1    Mitoma, I.2
  • 4
    • 0002171899 scopus 로고
    • The energy representation of Sobolev Lie groups
    • S. Albeverio and R. Hoegh-Krohn, "The energy representation of Sobolev Lie groups", Compositio Math. 36 (1978) 37-52.
    • (1978) Compositio Math. , vol.36 , pp. 37-52
    • Albeverio, S.1    Hoegh-Krohn, R.2
  • 5
    • 0010950066 scopus 로고
    • Construction of a rotational invariant diffusion on the free loop space
    • S. Albeverio, R. Léandre and M. Rockner, "Construction of a rotational invariant diffusion on the free loop space", C.R.A.S. t 316. Série I (1993) 287-292.
    • (1993) C.R.A.S. t , vol.316 , Issue.SERIE I , pp. 287-292
    • Albeverio, S.1    Léandre, R.2    Rockner, M.3
  • 8
    • 0001502193 scopus 로고
    • New invariants of 3 and 4 dimensional manifolds
    • M. Atiyah, "New invariants of 3 and 4 dimensional manifolds", Proc. Symposia in Pure Math. 48 (1988) 285-299.
    • (1988) Proc. Symposia in Pure Math. , vol.48 , pp. 285-299
    • Atiyah, M.1
  • 9
    • 84972570445 scopus 로고
    • Zéros d'un champ de vecteurs et classes caractéristiques équivariantes
    • N. Berline and M. Vergne, "Zéros d'un champ de vecteurs et classes caractéristiques équivariantes", Duke Math. J. 50 (1983) 539-548.
    • (1983) Duke Math. J. , vol.50 , pp. 539-548
    • Berline, N.1    Vergne, M.2
  • 10
    • 0003203464 scopus 로고
    • Large deviations and the Malliavin Calculus
    • Birkhauser
    • J. M. Bismut, "Large deviations and the Malliavin Calculus", Progress in Math. 45 Birkhauser (1984).
    • (1984) Progress in Math. , vol.45
    • Bismut, J.M.1
  • 11
    • 0002876396 scopus 로고
    • The Atiyah-Singer theorem: A probabilistic approach
    • J. M. Bismut, "The Atiyah-Singer theorem: A probabilistic approach", J.F.A. 57 (1984) 56-99.
    • (1984) J.F.A. , vol.57 , pp. 56-99
    • Bismut, J.M.1
  • 12
    • 0000695994 scopus 로고
    • The Lefschetz fixed point formulas
    • J. M. Bismut, "The Lefschetz fixed point formulas", J.F.A. 57 (1984) 329-348.
    • (1984) J.F.A. , vol.57 , pp. 329-348
    • Bismut, J.M.1
  • 13
    • 0000715107 scopus 로고
    • Index theorem and equivariant cohomology on the loop space
    • J. M. Bismut, "Index theorem and equivariant cohomology on the loop space", C.M.P. 98 (1985) 213-237.
    • (1985) C.M.P. , vol.98 , pp. 213-237
    • Bismut, J.M.1
  • 14
    • 11144249862 scopus 로고
    • Localisation formulas, superconnections and the index theorem for families
    • J. M. Bismut, "Localisation formulas, superconnections and the index theorem for families", C.M.P. 103 (1986) 127-166.
    • (1986) C.M.P. , vol.103 , pp. 127-166
    • Bismut, J.M.1
  • 15
    • 84972541701 scopus 로고
    • The Witten complex and the degenerate Morse inequalities
    • J. M. Bismut, "The Witten complex and the degenerate Morse inequalities", J. Diff. Geom. 23 (1986) 207-240.
    • (1986) J. Diff. Geom. , vol.23 , pp. 207-240
    • Bismut, J.M.1
  • 16
    • 21144471067 scopus 로고
    • The pfaffian line bundle
    • D. Borthwick, "The pfaffian line bundle", C.M.P. 149 (1992) 463-493.
    • (1992) C.M.P. , vol.149 , pp. 463-493
    • Borthwick, D.1
  • 17
    • 0007343563 scopus 로고
    • Loop spaces, characteristic classes and geometric quantization
    • Birkhauser
    • J. L. Brylinski, "Loop spaces, characteristic classes and geometric quantization", Progress in Math. 107, Birkhauser (1992).
    • (1992) Progress in Math. , vol.107
    • Brylinski, J.L.1
  • 18
    • 0000672090 scopus 로고
    • String structure and the path fibration of a group
    • A. L. Carey and M. K. Murray, "String structure and the path fibration of a group", C.M.P. 141 (1991) 441-452.
    • (1991) C.M.P. , vol.141 , pp. 441-452
    • Carey, A.L.1    Murray, M.K.2
  • 19
    • 0001646292 scopus 로고
    • Iterated path integrals of differential forms and loop space homology
    • K. T. Chen, "Iterated path integrals of differential forms and loop space homology", Ann. Math. 97 (1973) 213-237.
    • (1973) Ann. Math. , vol.97 , pp. 213-237
    • Chen, K.T.1
  • 21
    • 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 (1988) 519-548.
    • (1988) K-theory , vol.1 , pp. 519-548
    • Connes, A.1
  • 22
    • 0000833560 scopus 로고
    • String structures on loop bundles
    • R. Coquereaux and K. Pilch, "String structures on loop bundles", C.M.P. 120 (1989) 353-378.
    • (1989) C.M.P. , vol.120 , pp. 353-378
    • Coquereaux, R.1    Pilch, K.2
  • 23
    • 85037778538 scopus 로고    scopus 로고
    • Measures and differential equations in infinite dimensional spaces
    • Y. Dalecky and V. I. Fomin, "Measures and differential equations in infinite dimensional spaces", Maths. and Appl., Nauka.
    • Maths. and Appl., Nauka.
    • Dalecky, Y.1    Fomin, V.I.2
  • 25
    • 44049121803 scopus 로고
    • A Cameron-Martin type quasi-invariance formula for Brownian motion on compact manifolds
    • B. Driver, "A Cameron-Martin type quasi-invariance formula for Brownian motion on compact manifolds", J.F.A. 110 (1992) 272-376.
    • (1992) J.F.A. , vol.110 , pp. 272-376
    • Driver, B.1
  • 26
    • 0001010672 scopus 로고
    • Construction of diffusions on path and loop spaces of compact Riemannian manifolds
    • B. Driver and M. Rockner, "Construction of diffusions on path and loop spaces of compact Riemannian manifolds", C.R.A.S. t 315. Série I. (1992) 603-608.
    • (1992) C.R.A.S. t , vol.315 , Issue.SERIE I , pp. 603-608
    • Driver, B.1    Rockner, M.2
  • 28
    • 0003264261 scopus 로고
    • Stochastic differential equations on manifolds
    • Cambridge Univ. Press
    • D. Elworthy, "Stochastic differential equations on manifolds", L.M.S. Lectures Notes Serie 20, Cambridge Univ. Press, 1982.
    • (1982) L.M.S. Lectures Notes , Issue.SERIE 20
    • Elworthy, D.1
  • 29
    • 58149364652 scopus 로고
    • Towards a Riemannian geometry on the path space over a Riemannian manifold
    • O. Enchev and D. W. Stoock, "Towards a Riemannian geometry on the path space over a Riemannian manifold", J.F.A. 134 (1995) 392-416.
    • (1995) J.F.A. , vol.134 , pp. 392-416
    • Enchev, O.1    Stoock, D.W.2
  • 30
    • 0010885669 scopus 로고
    • Stochastic analysis on the path space of a Riemannian manifold
    • S. Fang and P. Malliavin, "Stochastic analysis on the path space of a Riemannian manifold", I.J.F.A. 118 (1993) 339-373.
    • (1993) I.J.F.A. , vol.118 , pp. 339-373
    • Fang, S.1    Malliavin, P.2
  • 33
    • 44949284398 scopus 로고
    • Differential forms on a loop space and the cyclic bar complex
    • E. Getzler, J. D. S. Jones and S. Petrack, "Differential forms on a loop space and the cyclic bar complex", Topology 30 (1991) 339-373.
    • (1991) Topology , vol.30 , pp. 339-373
    • Getzler, E.1    Jones, J.D.S.2    Petrack, S.3
  • 34
    • 84891338968 scopus 로고    scopus 로고
    • Invariance theory, the heat equation and the Atiyah-Singer theorem
    • Publish and Perish
    • P. B. Gilkey, "Invariance theory, the heat equation and the Atiyah-Singer theorem", Math. Lect. Series. 11, Publish and Perish.
    • Math. Lect. Series , vol.11
    • Gilkey, P.B.1
  • 35
    • 0000464861 scopus 로고
    • Potential theory on Hilbert spaces
    • L. Gross L. "Potential theory on Hilbert spaces", J.F.A. 1 (1967) 123-181.
    • (1967) J.F.A. , vol.1 , pp. 123-181
    • Gross, L.1
  • 36
    • 0039018517 scopus 로고
    • The supersymmetric sigma model, topological quantum mechanics and knot invariants
    • J. M. Guilarte, "The supersymmetric sigma model, topological quantum mechanics and knot invariants", J. Geom. Phys. 7 (1990) 255-302.
    • (1990) J. Geom. Phys. , vol.7 , pp. 255-302
    • Guilarte, J.M.1
  • 38
    • 0002223063 scopus 로고
    • Elliptic genera of level N for complex manifolds
    • eds. K. Bleuler and M. Werner, Kluwer
    • F. Hirzebruch, "Elliptic genera of level N for complex manifolds", in Differential Geometrical Methods in Theoretical Physics, eds. K. Bleuler and M. Werner, Kluwer, 1988, 37-63.
    • (1988) Differential Geometrical Methods in Theoretical Physics , pp. 37-63
    • Hirzebruch, F.1
  • 39
    • 0000725915 scopus 로고
    • Relativistic quantum statistical mechanics in 2 dimensional space time
    • R. Hoegh-Krohn, "Relativistic quantum statistical mechanics in 2 dimensional space time", C.M.P. 38 (1974) 195-224.
    • (1974) C.M.P. , vol.38 , pp. 195-224
    • Hoegh-Krohn, R.1
  • 44
    • 0002583382 scopus 로고
    • Index of a family of Dirac operators on loop spaces
    • A. Jaffe, A. Lesniewski and J. Weitsman, "Index of a family of Dirac operators on loop spaces", C.M.P. 112 (1987) 75-88.
    • (1987) C.M.P. , vol.112 , pp. 75-88
    • Jaffe, A.1    Lesniewski, A.2    Weitsman, J.3
  • 46
    • 0000438918 scopus 로고
    • p Chen forms on loop spaces
    • eds. M. Barlow and N. Bingham, Cambridge Univ. Press
    • p Chen forms on loop spaces", in Stochastic Analysis, eds. M. Barlow and N. Bingham, Cambridge Univ. Press, 1991, 104-162.
    • (1991) Stochastic Analysis , pp. 104-162
    • Jones, J.D.S.1    Léandre, R.2
  • 49
    • 0001373319 scopus 로고
    • World-sheet anomalies and loop geometry
    • T. Killingback, "World-sheet anomalies and loop geometry", Nucl. Phys. B288 (1987) 578-588.
    • (1987) Nucl. Phys. , vol.B288 , pp. 578-588
    • Killingback, T.1
  • 50
    • 0039771032 scopus 로고
    • La théorie des distributions en dimension quelquonque et l'intégration stochastique
    • P. Korezlioglu and S. Ustunel, L.N. in Maths., Springer
    • P. Krée, "La théorie des distributions en dimension quelquonque et l'intégration stochastique", in Stochastic Analysis, eds. P. Korezlioglu and S. Ustunel, L.N. in Maths., Springer, 1988, 170-233.
    • (1988) Stochastic Analysis , pp. 170-233
    • Krée, P.1
  • 51
    • 84966234236 scopus 로고
    • Diffusion and Brownian motion on infinite dimensional manifolds
    • H. H. Kuo, "Diffusion and Brownian motion on infinite dimensional manifolds", Trans. Amer. Math. Soc. 159 (1972) 439-452.
    • (1972) Trans. Amer. Math. Soc. , vol.159 , pp. 439-452
    • Kuo, H.H.1
  • 53
    • 0002435167 scopus 로고
    • More recent theory of Malliavin Calculus
    • S. Kusuoka, "More recent theory of Malliavin Calculus", Sugaku 5.2. (1992) 155-173.
    • (1992) Sugaku , vol.5 , Issue.2 , pp. 155-173
    • Kusuoka, S.1
  • 54
    • 0001285840 scopus 로고
    • Applications quantitatives et qualitatives du calcul de Malliavin. Col. Franco japonais
    • eds. M. Métivier and S. Watanabe
    • R. Léandre, "Applications quantitatives et qualitatives du Calcul de Malliavin. Col. Franco Japonais", eds. M. Métivier and S. Watanabe, L.N.M. 1322 (1988) 109-133; English translation: "Geometry of random motion", eds. R. Durrett and M. Pinsky, Contemporary Math. 73 (1988) 173-197.
    • (1988) L.N.M. , vol.1322 , pp. 109-133
    • Léandre, R.1
  • 55
    • 0001713180 scopus 로고
    • Geometry of random motion
    • R. Léandre, "Applications quantitatives et qualitatives du Calcul de Malliavin. Col. Franco Japonais", eds. M. Métivier and S. Watanabe, L.N.M. 1322 (1988) 109-133; English translation: "Geometry of random motion", eds. R. Durrett and M. Pinsky, Contemporary Math. 73 (1988) 173-197.
    • (1988) Contemporary Math. , vol.73 , pp. 173-197
    • Durrett, R.1    Pinsky, M.2
  • 56
    • 0000252704 scopus 로고
    • Integration by parts and rotationally invariant Sobolev Calculus on free loop spaces
    • XXVIII Winter School of Theoretical Physics, eds. R. Gielerak and Borowiec
    • R. Léandre, "Integration by parts and rotationally invariant Sobolev Calculus on free loop spaces", XXVIII Winter School of Theoretical Physics, eds. R. Gielerak and Borowiec, J. Geom. and Phys. 11 (1993) 517-528.
    • (1993) J. Geom. and Phys. , vol.11 , pp. 517-528
    • Léandre, R.1
  • 57
    • 0040082432 scopus 로고    scopus 로고
    • Invariant Sobolev Calculus on free loop space
    • R. Léandre, "Invariant Sobolev Calculus on free loop space", Acta Appl. Math. 46 (1997) 267-350.
    • (1997) Acta Appl. Math. , vol.46 , pp. 267-350
    • Léandre, R.1
  • 58
    • 0001090431 scopus 로고
    • Brownian motion over a Kahler manifold and elliptic genera of level N
    • eds. R. Sénéor and L. Streit, Nato Asi Series, Kluwer
    • R. Léandre, "Brownian motion over a Kahler manifold and elliptic genera of level N", in Stochastic Analysis and Applications in Physics, eds. R. Sénéor and L. Streit, Nato Asi Series, Kluwer, 1994, 193-219.
    • (1994) Stochastic Analysis and Applications in Physics , pp. 193-219
    • Léandre, R.1
  • 59
    • 0038897891 scopus 로고    scopus 로고
    • Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entiere
    • Séminaire de Probabilités XXX in Honour of P. A. Meyer and J. Neveu, eds. J. Azéma, M. Emery and M. Yor
    • R. Léandre, "Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entiere", Séminaire de Probabilités XXX in Honour of P. A. Meyer and J. Neveu, eds. J. Azéma, M. Emery and M. Yor, L.N.M. 1626 (1996) 68-100.
    • (1996) L.N.M. , vol.1626 , pp. 68-100
    • Léandre, R.1
  • 60
    • 0040082433 scopus 로고    scopus 로고
    • Brownian cohomology of an homogeneous manifold
    • eds. K. D. Elworthy, S. Kusuoka and I. Shigekawa, World Scientific
    • R. Léandre, "Brownian cohomology of an homogeneous manifold", in New Trends in Stochastic Analysis, eds. K. D. Elworthy, S. Kusuoka and I. Shigekawa, World Scientific, 1997, 305-347.
    • (1997) New Trends in Stochastic Analysis , pp. 305-347
    • Léandre, R.1
  • 61
    • 85037762511 scopus 로고    scopus 로고
    • String structure over the Brownian bridge
    • R. Léandre, "String structure over the Brownian bridge", to be published in J. Math. Phys.
    • J. Math. Phys.
    • Léandre, R.1
  • 62
    • 0040304520 scopus 로고    scopus 로고
    • Hilbert space of spinor fields over the free loop space
    • R. Léandre, "Hilbert space of spinor fields over the free loop space", Rev. Math. Phys. 9.2. (1997) 243-277.
    • (1997) Rev. Math. Phys. , vol.9 , Issue.2 , pp. 243-277
    • Léandre, R.1
  • 63
    • 84891295914 scopus 로고
    • Stochastic Moore loop space
    • Chaos, eds. P. Garbaczewski, M. Wolf and A. Weron
    • R. Léandre, "Stochastic Moore loop space", in Chaos, eds. P. Garbaczewski, M. Wolf and A. Weron, Lectures Notes in Phys. 457 (1995) 479-501.
    • (1995) Lectures Notes in Phys. , vol.457 , pp. 479-501
    • Léandre, R.1
  • 64
    • 0031093620 scopus 로고    scopus 로고
    • Stochastic Wess-Zumino-Witten model over a symplectic manifold
    • R. Léandre, "Stochastic Wess-Zumino-Witten model over a symplectic manifold", J. Geom. and Phys. 21 (1997) 307-336.
    • (1997) J. Geom. and Phys. , vol.21 , pp. 307-336
    • Léandre, R.1
  • 65
    • 4243810380 scopus 로고    scopus 로고
    • Stochastic Wess-Zumino-Witten models
    • Supersymmetry and Quantum Field Theory, eds. J. Wess and V. Akulov
    • R. Léandre, "Stochastic Wess-Zumino-Witten models", in Supersymmetry and Quantum Field Theory, eds. J. Wess and V. Akulov, Lecture Notes Phys. 509 (1998) 196-201.
    • (1998) Lecture Notes Phys. , vol.509 , pp. 196-201
    • Léandre, R.1
  • 66
    • 0040675988 scopus 로고    scopus 로고
    • Integration by parts and Cameron-Martin formulas for the free path space of a compact Riemannian manifold
    • Séminaire de Probabilités XXXI, eds. J. Azéma, M. Emery and M. Yor
    • R. Léandre and J. Norris, "Integration by parts and Cameron-Martin formulas for the free path space of a compact Riemannian manifold", Séminaire de Probabilités XXXI, eds. J. Azéma, M. Emery and M. Yor, L.N.M. 1655 (1997) 16-23.
    • (1997) L.N.M. , vol.1655 , pp. 16-23
    • Léandre, R.1    Norris, J.2
  • 67
    • 0010805441 scopus 로고
    • A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold
    • R. Léandre and S. S. Roan, "A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold", J. Geom. and Phys. 16 (1995) 71-98.
    • (1995) J. Geom. and Phys. , vol.16 , pp. 71-98
    • Léandre, R.1    Roan, S.S.2
  • 70
    • 84973997896 scopus 로고
    • Orientation and string structures on loop spaces
    • D. Mac Laughlin, "Orientation and string structures on loop spaces", Pac. J. Math. 155 (1992) 143-156.
    • (1992) Pac. J. Math. , vol.155 , pp. 143-156
    • Mac Laughlin, D.1
  • 71
    • 0001918078 scopus 로고
    • Integration on loop group III. Asymptotic Peter-Weyl orthogonality
    • M. P. Malliavin and P. Malliavin, "Integration on loop group III. Asymptotic Peter-Weyl orthogonality", J.F.A. 108 (1992) 13-46.
    • (1992) J.F.A. , vol.108 , pp. 13-46
    • Malliavin, M.P.1    Malliavin, P.2
  • 72
    • 0039178583 scopus 로고
    • Le calcul de Malliavin et un peu de pédagogie
    • Université de Strasbourg
    • P. A. Meyer, "Le calcul de Malliavin et un peu de pédagogie", R.C.P. 34 Université de Strasbourg, 1984.
    • (1984) R.C.P. , vol.34
    • Meyer, P.A.1
  • 73
    • 0000859132 scopus 로고
    • On the structure of Hopf algebras
    • J. W. Milnor and J. C. Moore, "On the structure of Hopf algebras", Ann. Math. 81 (1965) 211-264.
    • (1965) Ann. Math. , vol.81 , pp. 211-264
    • Milnor, J.W.1    Moore, J.C.2
  • 75
    • 58149364016 scopus 로고
    • Twisted sheets
    • J. Norris, "Twisted sheets", J.F.A. 132 (1995) 273-334.
    • (1995) J.F.A. , vol.132 , pp. 273-334
    • Norris, J.1
  • 76
    • 0000863870 scopus 로고
    • On the Arnold conjecture for weakly monotone symplectic manifolds
    • K. Ono, "On the Arnold conjecture for weakly monotone symplectic manifolds", Inventiones Math. 119 (1995) 519-537.
    • (1995) Inventiones Math. , vol.119 , pp. 519-537
    • Ono, K.1
  • 80
    • 0001514503 scopus 로고
    • Transformations of Brownian motion on a Riemannian symmetric space
    • I. Shigekawa, "Transformations of Brownian motion on a Riemannian symmetric space", Z.W. 65 (1984) 493-522.
    • (1984) Z.W. , vol.65 , pp. 493-522
    • Shigekawa, I.1
  • 81
    • 0000448499 scopus 로고
    • De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
    • I. Shigekawa, "De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space", J. Math. Kyoto. Univ. 26 (1986) 191-202.
    • (1986) J. Math. Kyoto. Univ. , vol.26 , pp. 191-202
    • Shigekawa, I.1
  • 82
    • 26744439267 scopus 로고
    • Homologie associée une fonctionnelle (d'apres A. Floer)
    • J. C. Sikorav, "Homologie associée une fonctionnelle (d'apres A. Floer)", Séminaire Bourbaki. Expoé 733. Astérisque 201-203 (1991) 115-141.
    • (1991) Séminaire Bourbaki. Expoé 733. Astérisque , vol.201-203 , pp. 115-141
    • Sikorav, J.C.1
  • 83
    • 0000523790 scopus 로고
    • De Rham currents and Stoke's formula in a Hilbert space
    • O. G. Smolyanov, "De Rham currents and Stoke's formula in a Hilbert space", Soviet Math. Dok. 33.3. (1986) 140-144.
    • (1986) Soviet Math. Dok. , vol.33 , Issue.3 , pp. 140-144
    • Smolyanov, O.G.1
  • 84
    • 0001598675 scopus 로고
    • 1 actions and elliptic genera
    • 1 actions and elliptic genera", C.M.P. 122 (1989) 455-526.
    • (1989) C.M.P. , vol.122 , pp. 455-526
    • Taubes, C.1
  • 86
    • 0002569742 scopus 로고
    • Stochastic analysis and its applications
    • S. Watanabe, "Stochastic analysis and its applications", Sugaku 5.1. (1992) 51-71.
    • (1992) Sugaku , vol.5 , Issue.1 , pp. 51-71
    • Watanabe, S.1
  • 87
    • 84972500802 scopus 로고
    • Supersymmetry and Morse theory
    • E. Witten, "Supersymmetry and Morse theory", J. Diff. Geom. 17 (1982) 661-692.
    • (1982) J. Diff. Geom. , vol.17 , pp. 661-692
    • Witten, E.1
  • 88
    • 0002045062 scopus 로고
    • The index of the Dirac operator in loop space
    • ed. P. S. Landweber, L.N.M.
    • E. Witten, "The index of the Dirac operator in loop space", in Elliptic Curves and Modular forms in Algebraic Topology, ed. P. S. Landweber, L.N.M. 1326 (1988) 161-181.
    • (1988) Elliptic Curves and Modular Forms in Algebraic Topology , vol.1326 , pp. 161-181
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.