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Volumn 201, Issue 2, 1999, Pages 249-290

Yang-Mills theory and the Segal-Bargmann transform

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EID: 0033246638     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050555     Document Type: Article
Times cited : (52)

References (45)
  • 2
    • 0001036206 scopus 로고
    • Irreducibility and reducibility for the energy representation of the group of mappings of a Riemannian manifold into a compact semisimple Lie group
    • [AKT] Albeverio, S., Hoegh-Krohn, R., and Testard, D.: Irreducibility and reducibility for the energy representation of the group of mappings of a Riemannian manifold into a compact semisimple Lie group. J. Funct. Anal. 41, 378-396 (1981)
    • (1981) J. Funct. Anal. , vol.41 , pp. 378-396
    • Albeverio, S.1    Hoegh-Krohn, R.2    Testard, D.3
  • 5
    • 84980077803 scopus 로고
    • On a Hilbert space of analytic functions and an associated integral transform, Part I
    • [B] Bargmann, V.: On a Hilbert space of analytic functions and an associated integral transform, Part I. Comm. Pure Appl. Math. 14, 187-214 (1961)
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 187-214
    • Bargmann, V.1
  • 6
    • 0030304691 scopus 로고    scopus 로고
    • Canonical quantization of Yang-Mills on a circle
    • [Di] Dimock, J.: Canonical quantization of Yang-Mills on a circle. Rev. Math. Phys. 8, 85-102 (1996)
    • (1996) Rev. Math. Phys. , vol.8 , pp. 85-102
    • Dimock, J.1
  • 7
    • 0001724972 scopus 로고
    • Classifications of bundle connection pairs by parallel translation and lassos
    • [D1] Driver, B.: Classifications of bundle connection pairs by parallel translation and lassos. J. Func. Anal. 83, 185-231 (1989)
    • (1989) J. Func. Anal. , vol.83 , pp. 185-231
    • Driver, B.1
  • 8
    • 0002285687 scopus 로고
    • On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms
    • [D2] Driver, B.: On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms. J. Funct. Anal. 133, 69-128 (1995)
    • (1995) J. Funct. Anal. , vol.133 , pp. 69-128
    • Driver, B.1
  • 9
    • 0002523116 scopus 로고    scopus 로고
    • Hilbert spaces of holomorphic functions on complex Lie groups
    • Elworthy, K., Kusuoka, S., Shigekawa, I. (eds.) Singapore: World Scientific
    • [DG] Driver, B., and Gross, L.: Hilbert spaces of holomorphic functions on complex Lie groups. In: Elworthy, K., Kusuoka, S., Shigekawa, I. (eds.) New trends in stochastic analysis. Proceedings of a Taniguchi international workshop, Singapore: World Scientific, 1997, pp. 76-106
    • (1997) New Trends in Stochastic Analysis. Proceedings of a Taniguchi International Workshop , pp. 76-106
    • Driver, B.1    Gross, L.2
  • 12
    • 0030587376 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for pinned loop groups
    • [DL] Driver, B., and Lohrenz, T.: Logarithmic Sobolev inequalities for pinned loop groups. J. Funct. Anal. 140, 381-448 (1996)
    • (1996) J. Funct. Anal. , vol.140 , pp. 381-448
    • Driver, B.1    Lohrenz, T.2
  • 13
    • 0003264261 scopus 로고
    • Stochastic differential equations on manifolds
    • Cambridge: Cambridge Univ. Press
    • [E1] Elworthy, K.: Stochastic differential equations on manifolds. London Mathematical Society Lecture Note Series, 70, Cambridge: Cambridge Univ. Press, 1982
    • (1982) London Mathematical Society Lecture Note Series , vol.70
    • Elworthy, K.1
  • 15
    • 84972518061 scopus 로고
    • The geometry of loop groups
    • [F] Freed, D.: The geometry of loop groups. J. Diff. Geom. 28, 223-276 (1988)
    • (1988) J. Diff. Geom. , vol.28 , pp. 223-276
    • Freed, D.1
  • 16
    • 0000521725 scopus 로고
    • Representations of the group of functions taking values in a compact Lie group
    • [GGV] Gelfand, I., Graev, M., and Vershik, A.: Representations of the group of functions taking values in a compact Lie group. Compositio Math. 42, 217-243 (1980/81)
    • (1980) Compositio Math. , vol.42 , pp. 217-243
    • Gelfand, I.1    Graev, M.2    Vershik, A.3
  • 17
    • 0001572330 scopus 로고
    • Uniqueness of ground states for Schrödinger operators over loop groups
    • [G] Gross, L.: Uniqueness of ground states for Schrödinger operators over loop groups. J. Funct. Anal. 112, 373-441 (1993)
    • (1993) J. Funct. Anal. , vol.112 , pp. 373-441
    • Gross, L.1
  • 18
    • 0001976103 scopus 로고    scopus 로고
    • Hall's transform and the Segal-Bargmann map
    • Fukushima, M., Ikeda, N., Kunita, H., and Watanabe, S. (eds.) Berlin-New York: Springer-Verlag
    • [GM] Gross, L., and Malliavin, P.: Hall's transform and the Segal-Bargmann map. In: Fukushima, M., Ikeda, N., Kunita, H., and Watanabe, S. (eds.) Itô's stochastic calculus and probability theory, Berlin-New York: Springer-Verlag, 1996, pp. 73-116
    • (1996) Itô's Stochastic Calculus and Probability Theory , pp. 73-116
    • Gross, L.1    Malliavin, P.2
  • 19
    • 0000374308 scopus 로고
    • The Segal-Bargmann "coherent state" transform for compact Lie groups
    • [H1] Hall, B.: The Segal-Bargmann "coherent state" transform for compact Lie groups. J. Funct. Anal. 122, 103-151 (1994)
    • (1994) J. Funct. Anal. , vol.122 , pp. 103-151
    • Hall, B.1
  • 20
    • 0030672169 scopus 로고    scopus 로고
    • The inverse Segal-Bargmann transform for compact Lie groups
    • [H2] Hall, B.: The inverse Segal-Bargmann transform for compact Lie groups. J. Funct. Anal. 143, 98-116 (1997)
    • (1997) J. Funct. Anal. , vol.143 , pp. 98-116
    • Hall, B.1
  • 21
    • 0031546438 scopus 로고    scopus 로고
    • Phase space bounds for quantum mechanics on a compact Lie group
    • [H3] Hall, B.: Phase space bounds for quantum mechanics on a compact Lie group. Commun. Math. Phys. 184, 233-250 (1997)
    • (1997) Commun. Math. Phys. , vol.184 , pp. 233-250
    • Hall, B.1
  • 22
    • 0002432665 scopus 로고    scopus 로고
    • Quantum mechanics in phase space
    • [H4] Hall, B.: Quantum mechanics in phase space. Contemp. Math. 214, 47-62 (1998)
    • (1998) Contemp. Math. , vol.214 , pp. 47-62
    • Hall, B.1
  • 24
    • 0001498713 scopus 로고    scopus 로고
    • The Segal-Bargmann transform for path-groups
    • [HS] Hall, B., and Sengupta, A.: The Segal-Bargmann transform for path-groups. J. Funct. Anal. 152, 220-254 (1998)
    • (1998) J. Funct. Anal. , vol.152 , pp. 220-254
    • Hall, B.1    Sengupta, A.2
  • 26
    • 0001944057 scopus 로고
    • Chaos de wiener et intégrale de feynman
    • Séminaire de Probabilités, XXII. Berlin-New York: Springer-Verlag
    • [HM] Hu, Y., and Meyer, P.-A.: Chaos de Wiener et intégrale de Feynman. In: Séminaire de Probabilités, XXII. Lecture Notes in Math., 1321, Berlin-New York: Springer-Verlag, 1988, pp. 51-71
    • (1988) Lecture Notes in Math. , vol.1321 , pp. 51-71
    • Hu, Y.1    Meyer, P.-A.2
  • 28
    • 84972503912 scopus 로고
    • Multiple Wiener integral
    • [Ito] Itô, K.: Multiple Wiener integral. J. Math. Soc. Japan 3, 157-169 (1951)
    • (1951) J. Math. Soc. Japan , vol.3 , pp. 157-169
    • Itô, K.1
  • 30
    • 0001702220 scopus 로고
    • Determination of the spectrum of the flow of Brownian motion
    • [Ka] Kakutani, S.: Determination of the spectrum of the flow of Brownian motion. Proc. Nat. Acad. Sci. U.S.A. 36, 319-323 (1950)
    • (1950) Proc. Nat. Acad. Sci. U.S.A. , vol.36 , pp. 319-323
    • Kakutani, S.1
  • 31
    • 0003522827 scopus 로고
    • Cambridge Studies in Advanced Mathematics, Cambridge: Cambridge Univ. Press
    • [Ku] Kunita, H.: Stochastic flows and stochastic differential equations. Cambridge Studies in Advanced Mathematics, 24, Cambridge: Cambridge Univ. Press, 1990
    • (1990) Stochastic Flows and Stochastic Differential Equations , vol.24
    • Kunita, H.1
  • 33
    • 0031556438 scopus 로고    scopus 로고
    • Constrained quantization and θ-angles
    • [LW] Landsman, N., and Wren, K.: Constrained quantization and θ-angles. Nucl. Phys. B 502, 537-560 (1997)
    • (1997) Nucl. Phys. B , vol.502 , pp. 537-560
    • Landsman, N.1    Wren, K.2
  • 34
    • 0001386011 scopus 로고
    • Morse theory on Hilbert manifolds
    • [P] Palais, R.: Morse theory on Hilbert manifolds. Topology 2, 299-340 (1963)
    • (1963) Topology , vol.2 , pp. 299-340
    • Palais, R.1
  • 35
    • 0040124932 scopus 로고
    • Yang-Mills theory on a cylinder
    • [Ra] Rajeev, S.: Yang-Mills theory on a cylinder. Phys. Lett. B 212, 203-205 (1988)
    • (1988) Phys. Lett. B , vol.212 , pp. 203-205
    • Rajeev, S.1
  • 36
    • 21844506809 scopus 로고
    • Some rigorous results for Yang-Mills theories on a cylinder
    • [RR] Rajeev, S., and Rossi, L.: Some rigorous results for Yang-Mills theories on a cylinder. J. Math. Phys. 36, 3308-3319 (1995)
    • (1995) J. Math. Phys. , vol.36 , pp. 3308-3319
    • Rajeev, S.1    Rossi, L.2
  • 37
    • 21344460008 scopus 로고
    • Equivalence-singularity dichotomy for the Wiener measures on path groups and loop groups
    • [Sa1] Sadasue, G.: Equivalence-singularity dichotomy for the Wiener measures on path groups and loop groups. J. Math. Kyoto Univ. 35, 653-662 (1995)
    • (1995) J. Math. Kyoto Univ. , vol.35 , pp. 653-662
    • Sadasue, G.1
  • 40
    • 84972505242 scopus 로고
    • Mathematical characterization of the physical vacuum for a linear Bose-Einstein field
    • [S2] Segal, I.: Mathematical characterization of the physical vacuum for a linear Bose-Einstein field. Illinois J. Math. 6, 500-523 (1962)
    • (1962) Illinois J. Math. , vol.6 , pp. 500-523
    • Segal, I.1
  • 41
    • 0000663904 scopus 로고
    • The complex wave representation of the free Boson field
    • Gohberg, I. and Kac, M. (eds.) Topics in functional analysis. Essays dedicated to M. G. Krein on the occasion of his 70th birthday , New York: Academic Press
    • [S3] Segal, I.: The complex wave representation of the free Boson field. In: Gohberg, I. and Kac, M. (eds.) Topics in functional analysis. Essays dedicated to M. G. Krein on the occasion of his 70th birthday. Advances in Mathematics Supplementary Studies, Vol. 3, New York: Academic Press, 1978, pp. 321-343
    • (1978) Advances in Mathematics Supplementary Studies , vol.3 , pp. 321-343
    • Segal, I.1
  • 42
    • 84957129238 scopus 로고
    • On explicit formulas for solutions of stochastic equations
    • [VK] Veretennikov, A., and Krylov, N.: On explicit formulas for solutions of stochastic equations. Math. U.S.S.R. Sbornic 29, 239-256 (1976)
    • (1976) Math. U.S.S.R. Sbornic , vol.29 , pp. 239-256
    • Veretennikov, A.1    Krylov, N.2
  • 43
    • 0009031172 scopus 로고
    • On the irreducibility and inequivalence of unitary representations of gauge groups
    • [Wa] Wallach, N.: On the irreducibility and inequivalence of unitary representations of gauge groups. Compositio Math. 64, 3-29 (1987)
    • (1987) Compositio Math. , vol.64 , pp. 3-29
    • Wallach, N.1
  • 44
    • 0242310336 scopus 로고
    • On quantum gauge theories in two dimensions
    • [Wi] Witten, E.: On quantum gauge theories in two dimensions. Commun. Math. Phys. 141, 153-209 (1991)
    • (1991) Commun. Math. Phys. , vol.141 , pp. 153-209
    • Witten, E.1
  • 45
    • 0032558063 scopus 로고    scopus 로고
    • Constrained quantization and θ-angles II
    • [W] Wren, K.: Constrained quantization and θ-angles II. Nucl. Phys. B 521, 472-502 (1998)
    • (1998) Nucl. Phys. B , vol.521 , pp. 472-502
    • Wren, K.1


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