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Volumn 4, Issue 2, 2001, Pages 221-266

Renormalized Traces as a Looking Glass into Infinite-dimensional Geometry

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EID: 0035639886     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025701000486     Document Type: Article
Times cited : (15)

References (73)
  • 1
    • 0032472568 scopus 로고    scopus 로고
    • Regularisable and minimal orbits for group actions in infinite dimensions
    • M. Arnaudon and S. Paycha, Regularisable and minimal orbits for group actions in infinite dimensions, Comm. Math. Phys. 191 (1998) 641-662.
    • (1998) Comm. Math. Phys. , vol.191 , pp. 641-662
    • Arnaudon, M.1    Paycha, S.2
  • 2
    • 0031476397 scopus 로고    scopus 로고
    • Stochastic tools on Hubert manifolds; interplay with geometry and physics
    • M. Arnaudon and S. Paycha, Stochastic tools on Hubert manifolds; interplay with geometry and physics, Comm. Math. Phys. 187 (1998) 243-260.
    • (1998) Comm. Math. Phys. , vol.187 , pp. 243-260
    • Arnaudon, M.1    Paycha, S.2
  • 4
    • 11144249862 scopus 로고
    • Localization formulas, superconnections and the index theorem for families
    • J.-M. Bismut, Localization formulas, superconnections and the index theorem for families, Comm. Math. Phys. 103 (1986) 127-166.
    • (1986) Comm. Math. Phys. , vol.103 , pp. 127-166
    • Bismut, J.-M.1
  • 7
    • 34250127531 scopus 로고
    • The analysis of elliptic families I
    • J.-M. Bismut and D. Freed, The analysis of elliptic families I, Comm. Math. Phys. 106 (1986) 159-176; The analysis of elliptic families II, ibid. 107 (1986) 103-163.
    • (1986) Comm. Math. Phys. , vol.106 , pp. 159-176
    • Bismut, J.-M.1    Freed, D.2
  • 8
    • 33744647630 scopus 로고
    • The analysis of elliptic families II
    • J.-M. Bismut and D. Freed, The analysis of elliptic families I, Comm. Math. Phys. 106 (1986) 159-176; The analysis of elliptic families II, ibid. 107 (1986) 103-163.
    • (1986) Comm. Math. Phys. , vol.107 , pp. 103-163
  • 9
    • 0001304678 scopus 로고
    • On the determinant of elliptic differential and finite difference operators in vector bundles over S
    • D. Burghelea, L. Friedlander and T. Kappeler, On the determinant of elliptic differential and finite difference operators in vector bundles over S , Comm. Math. Phys. 138 (1991) 1-18.
    • (1991) Comm. Math. Phys. , vol.138 , pp. 1-18
    • Burghelea, D.1    Friedlander, L.2    Kappeler, T.3
  • 10
    • 0010299885 scopus 로고
    • Asymptotic pseudodifferential operators and index theory
    • J. Block and J. Fox, Asymptotic pseudodifferential operators and index theory, Cont. Math. 105 (1990) 1-32.
    • (1990) Cont. Math. , vol.105 , pp. 1-32
    • Block, J.1    Fox, J.2
  • 15
  • 18
    • 0346899686 scopus 로고    scopus 로고
    • Ph.D. thesis, in preparation
    • C. Ducourtioux, Ph.D. thesis, in preparation.
    • Ducourtioux, C.1
  • 19
    • 0030587376 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for pinned loop groups
    • B. Driver and T. Lohrenz, Logarithmic Sobolev inequalities for pinned loop groups, J. Funct. Anal. 140 (1996).
    • (1996) J. Funct. Anal. , vol.140
    • Driver, B.1    Lohrenz, T.2
  • 20
    • 0032474309 scopus 로고    scopus 로고
    • Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
    • E. Elizalde, L. Vanzo and S. Zerbini, Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue, Comm. Math. Phys. 194 (1998) 613-630.
    • (1998) Comm. Math. Phys. , vol.194 , pp. 613-630
    • Elizalde, E.1    Vanzo, L.2    Zerbini, S.3
  • 21
    • 84972518061 scopus 로고
    • The geometry of loop groups
    • D. Freed, The geometry of loop groups, J. Diff. Geom. 28 (1988) 223-276.
    • (1988) J. Diff. Geom. , vol.28 , pp. 223-276
    • Freed, D.1
  • 25
    • 0346269380 scopus 로고
    • Cyclic homology and the Atiyah-Patodi-Singer index theorem
    • Index Theory and Operator Algebras, eds. J. Fox and P. Haskell
    • E. Getzler, Cyclic homology and the Atiyah-Patodi-Singer index theorem, in Index Theory and Operator Algebras, Cont. Math., Vol. 148, eds. J. Fox and P. Haskell (1993), pp. 19-45.
    • (1993) Cont. Math. , vol.148 , pp. 19-45
    • Getzler, E.1
  • 26
    • 0000464861 scopus 로고
    • Potential theory on Hilbert space
    • L. Gross, Potential theory on Hilbert space, J. Funct. Anal. 1 (1967) 123-181.
    • (1967) J. Funct. Anal. , vol.1 , pp. 123-181
    • Gross, L.1
  • 29
    • 0002389669 scopus 로고    scopus 로고
    • Quantum harmonic analysis and geometric invariants
    • A. Jaffe, Quantum harmonic analysis and geometric invariants, Adv. Math. 143 (1999) 1-110.
    • (1999) Adv. Math. , vol.143 , pp. 1-110
    • Jaffe, A.1
  • 32
    • 0009107213 scopus 로고
    • Ward identities and noncommutative geometry
    • A. Jaffe and K. Osterwalder, Ward identities and noncommutative geometry, Comm. Math. Phys. 132 (1990) 119-130.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 119-130
    • Jaffe, A.1    Osterwalder, K.2
  • 33
    • 0000887782 scopus 로고
    • Le résidu non commutatif
    • Ch. Kassel, Le résidu non commutatif, Sérn. Bourbaki, Astér. 177 (1989) 199-229.
    • (1989) Sérn. Bourbaki, Astér. , vol.177 , pp. 199-229
    • Kassel, Ch.1
  • 34
    • 0010852977 scopus 로고
    • Submanifolds in path space
    • ed. K. Uhlenbeck Publish or Perish
    • C. King, C. L. Terng, Submanifolds in path space, in Global Analysis in Modern Mathematics, ed. K. Uhlenbeck (Publish or Perish, 1993), pp. 253-282.
    • (1993) Global Analysis in Modern Mathematics , pp. 253-282
    • King, C.1    Terng, C.L.2
  • 36
    • 0003073673 scopus 로고
    • Lévy Laplacians of generalized functions on a nuclear space
    • H. H. Kuo, N. Obata and K. Saito, Lévy Laplacians of generalized functions on a nuclear space, J. Funct. Anal. 94 (1990) 74-92.
    • (1990) J. Funct. Anal. , vol.94 , pp. 74-92
    • Kuo, H.H.1    Obata, N.2    Saito, K.3
  • 38
    • 0000396875 scopus 로고
    • Geometry of determinants of elliptic operators
    • eds. S. Gindikin, J. Lepowski and R. L. Wilson, Progress in Mathematics
    • M. Kontsevich, S. Vishik, Geometry of determinants of elliptic operators, in Functional Analysis on the Eve of the 21st Century, eds. S. Gindikin, J. Lepowski and R. L. Wilson, Progress in Mathematics (1994), Vol. 1.
    • (1994) Functional Analysis on the Eve of the 21st Century , vol.1
    • Kontsevich, M.1    Vishik, S.2
  • 39
    • 0003155949 scopus 로고
    • A central extension of the algebra of pseudodifferential symbols
    • O. S. Kravenchko and B. A. Khesin, A central extension of the algebra of pseudodifferential symbols, Funct. Anal. Appl. 25 (1991) 152-154.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 152-154
    • Kravenchko, O.S.1    Khesin, B.A.2
  • 40
    • 0000489418 scopus 로고
    • The homotopy of the unitary group of Hilbert spaces
    • N. H. Kuiper, The homotopy of the unitary group of Hilbert spaces, Topology 3 (1965) 19-30.
    • (1965) Topology , vol.3 , pp. 19-30
    • Kuiper, N.H.1
  • 41
    • 0003170935 scopus 로고    scopus 로고
    • On the noncommutative residue for pseudo-differential operators with logpolyhomogeneous symbols
    • M. Lesch, On the noncommutative residue for pseudo-differential operators with logpolyhomogeneous symbols, Ann. Global Anal. Geom. 17 (1999) 151-187.
    • (1999) Ann. Global Anal. Geom. , vol.17 , pp. 151-187
    • Lesch, M.1
  • 43
    • 0347530581 scopus 로고    scopus 로고
    • Ph.D thesis, in preparation
    • J. P. Magnot, Ph.D thesis, in preparation.
    • Magnot, J.P.1
  • 49
    • 0242452136 scopus 로고    scopus 로고
    • Second quantization, anomalies and group extensions
    • C.I.R.M, Luminy June
    • J. Mickelsson, Second quantization, anomalies and group extensions, Lecture notes given at the Colloque sur les Méthodes Géométriques en Physique, C.I.R.M, Luminy (June 1997); Wodzicki residue and anomalies on current algebras in Integrable Models and Strings, eds. A. Alekseev et al., Lecture Notes in Physics, Vol. 436 (Springer, 1994).
    • (1997) Lecture Notes Given at the Colloque Sur Les Méthodes Géométriques en Physique
    • Mickelsson, J.1
  • 50
    • 0007197512 scopus 로고
    • Wodzicki residue and anomalies on current algebras
    • Integrable Models and Strings, eds. A. Alekseev et al., Springer
    • J. Mickelsson, Second quantization, anomalies and group extensions, Lecture notes given at the Colloque sur les Méthodes Géométriques en Physique, C.I.R.M, Luminy (June 1997); Wodzicki residue and anomalies on current algebras in Integrable Models and Strings, eds. A. Alekseev et al., Lecture Notes in Physics, Vol. 436 (Springer, 1994).
    • (1994) Lecture Notes in Physics , vol.436
  • 52
    • 84973997943 scopus 로고
    • The multiplicative anomaly for determinants of elliptic operators
    • K. Okikiolu, The multiplicative anomaly for determinants of elliptic operators, Duke Math. J. 79 (1995) 723-750.
    • (1995) Duke Math. J. , vol.79 , pp. 723-750
    • Okikiolu, K.1
  • 55
    • 85058721803 scopus 로고    scopus 로고
    • Curvature on determinant bundles and first Chern forms
    • to appear
    • S. Paycha and S. Rosenberg, Curvature on determinant bundles and first Chern forms (to appear in J. Geom. Phys.).
    • J. Geom. Phys.
    • Paycha, S.1    Rosenberg, S.2
  • 58
    • 11244319351 scopus 로고
    • Determinants of Cauchy-Riemann operators over a Riemann surface
    • D. Quillen, Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985) 37-34.
    • (1985) Funct. Anal. Appl. , vol.19 , pp. 37-134
    • Quillen, D.1
  • 59
    • 0002757119 scopus 로고
    • Lie algebras of differential operators, their central extensions, and W-algebras
    • A. O. Radul, Lie algebras of differential operators, their central extensions, and W-algebras, Funct. Anal. Appl. 25 (1991) 25-39.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 25-39
    • Radul, A.O.1
  • 60
    • 0000119424 scopus 로고
    • R-torsion and the Laplacian on Riemann manifolds
    • D. B. Ray and T. M. Singer, R-torsion and the Laplacian on Riemann manifolds, Adv. Math. 7 (1971) 145-210.
    • (1971) Adv. Math. , vol.7 , pp. 145-210
    • Ray, D.B.1    Singer, T.M.2
  • 61
    • 0001124087 scopus 로고
    • Extensions centrales d'algèbres et de groupes de Lie de dimension infinie, algèbres de Virasoro et généralisations
    • Special Issue in Honour of K. Maurin
    • C. Roger, Extensions centrales d'algèbres et de groupes de Lie de dimension infinie, algèbres de Virasoro et généralisations, Rep. Math. Phys., Special Issue in Honour of K. Maurin (1995).
    • (1995) Rep. Math. Phys.
    • Roger, C.1
  • 63
    • 0346899689 scopus 로고    scopus 로고
    • On some new infinite-dimensional Laplacians
    • Seminar on Stochastic Analysis, Random Fields and Applications, ed. R. Dalang Birkhauser
    • S. Scarlatti, On some new infinite-dimensional Laplacians, in Seminar on Stochastic Analysis, Random Fields and Applications, Progress in Probability, Vol. 45, ed. R. Dalang (Birkhauser, 1999).
    • (1999) Progress in Probability , vol.45
    • Scarlatti, S.1
  • 65
    • 4243981140 scopus 로고
    • Field theory commutators
    • J. Schwinger, Field theory commutators, Phys. Rev. Lett. 3 (1959) 296-297.
    • (1959) Phys. Rev. Lett. , vol.3 , pp. 296-297
    • Schwinger, J.1
  • 66
    • 0001738999 scopus 로고
    • Complex powers of an elliptic operator
    • R. Seeley, Complex powers of an elliptic operator, A.M.S Proc. Symp. Pure Math. X (1967) 288-307.
    • (1967) A.M.S Proc. Symp. Pure Math. , vol.10 , pp. 288-307
    • Seeley, R.1
  • 68
    • 0034215751 scopus 로고    scopus 로고
    • Differential geometry of Grassmannian embeddings of based loop groups
    • M. Spera and T. Wurzbacher, Differential geometry of Grassmannian embeddings of based loop groups, Diff. Geom. Appl. 13 (2000) 43-75.
    • (2000) Diff. Geom. Appl. , vol.13 , pp. 43-75
    • Spera, M.1    Wurzbacher, T.2
  • 70
    • 0002794818 scopus 로고
    • Local invariants of spectral asymmetry
    • M. Wodzicki, Local invariants of spectral asymmetry, Inv. Math. 75 (1984) 143-178.
    • (1984) Inv. Math. , vol.75 , pp. 143-178
    • Wodzicki, M.1
  • 72
    • 0040475795 scopus 로고
    • Lévy Laplacians and Brownian particles in Hubert spaces
    • Y. N. Zhang, Lévy Laplacians and Brownian particles in Hubert spaces, J. Funct. Anal. 133 (1995) 425-441.
    • (1995) J. Funct. Anal. , vol.133 , pp. 425-441
    • Zhang, Y.N.1


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