메뉴 건너뛰기




Volumn 226, Issue 2, 2002, Pages 233-268

Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036005396     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200607     Document Type: Article
Times cited : (86)

References (55)
  • 2
    • 84980077803 scopus 로고
    • On a Hilbert space of analytic functions and an associated integral transform
    • [B]
    • [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) Part I. Comm. Pure Appl. Math. , vol.14 , pp. 187-214
    • Bargmann, V.1
  • 3
    • 0003277239 scopus 로고
    • Representations of compact Lie groups
    • [BtD] New York, Berlin: Springer-Verlag
    • [BtD] Bröcker, T. and tom Dieck, T: Representations of compact Lie groups. Graduate Texts in Mathematics 98. New York, Berlin: Springer-Verlag, 1995
    • (1995) Graduate Texts in Mathematics , vol.98
    • Bröcker, T.1    Tom Dieck, T.2
  • 4
    • 0001494149 scopus 로고
    • Coherent states over symplectic homogeneous spaces
    • [De]
    • [De] De Bièvre, S.: Coherent states over symplectic homogeneous spaces. J. Math. Phys. 30, 1401-1407 (1989)
    • (1989) J. Math. Phys. , vol.30 , pp. 1401-1407
    • De Bièvre, S.1
  • 5
    • 0002285687 scopus 로고
    • On the Kakutani-Itô-Segal-Gross and Segal-Bargmann-Hall isomorphisms
    • [Dr]
    • [Dr] 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
  • 6
    • 0033246638 scopus 로고    scopus 로고
    • Yang-Mills theory and the Segal-Bargmann transform
    • [DH]
    • [DH] Driver, B. and Hall, B.: Yang-Mills theory and the Segal-Bargmann transform. Commun. Math. Phys. 201, 249-290 (1999)
    • (1999) Commun. Math. Phys. , vol.201 , pp. 249-290
    • Driver, B.1    Hall, B.2
  • 8
    • 0013260994 scopus 로고
    • A Kähler structure on the punctured cotangent bundle of complex and quaternion projective spaces and its application to a geometric quantization. II
    • [FY]
    • [FY] Furutani, K. and Yoshizawa, S.: A Kähler structure on the punctured cotangent bundle of complex and quaternion projective spaces and its application to a geometric quantization. II. Japan. J. Math. (N.S.) 21, 355-392 (1995)
    • (1995) Japan. J. Math. (N.S.) , vol.21 , pp. 355-392
    • Furutani, K.1    Yoshizawa, S.2
  • 9
    • 0000320133 scopus 로고
    • Constraints, reduction, and quantization
    • [Go]
    • [Go] Gotay, M.: Constraints, reduction, and quantization. J. Math. Phys. 27, 2051-2066 (1986)
    • (1986) J. Math. Phys. , vol.27 , pp. 2051-2066
    • Gotay, M.1
  • 10
    • 0001572330 scopus 로고
    • Uniqueness of ground states for Schrödinger operators over loop groups
    • [G1]
    • [G1] 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
  • 12
    • 0001976103 scopus 로고    scopus 로고
    • Hall's transform and the Segal-Bargmann map
    • [GM] Fukushima, M., Ikeda, N., Kunita, H. and Watanabe, S., eds., New York, Berlin: Springer-Verlag
    • [GM] Gross, L. and Malliavin, P.: Hall's transform and the Segal-Bargmann map. In: Itô's stochastic calculus and probability theory, Fukushima, M., Ikeda, N., Kunita, H. and Watanabe, S., eds., New York, Berlin: Springer-Verlag, 1996, pp. 73-116
    • (1996) Itô's Stochastic Calculus and Probability Theory , pp. 73-116
    • Gross, L.1    Malliavin, P.2
  • 13
    • 84972536305 scopus 로고
    • Grauert tubes and the homogeneous Monge-Ampère equation
    • [GStenz1]
    • [GStenz1] Guillemin, V. and Stenzel, M.: Grauert tubes and the homogeneous Monge-Ampère equation. J. Differ. Geom. 34, 561-570 (1991)
    • (1991) J. Differ. Geom. , vol.34 , pp. 561-570
    • Guillemin, V.1    Stenzel, M.2
  • 14
    • 84972535629 scopus 로고
    • Grauert tubes and the homogeneous Monge-Ampère equation. II
    • [GStenz2]
    • [GStenz2] Guillemin, V. and Stenzel, M.: Grauert tubes and the homogeneous Monge-Ampère equation. II. J. Differ. Geom. 35, 627-641 (1992)
    • (1992) J. Differ. Geom. , vol.35 , pp. 627-641
    • Guillemin, V.1    Stenzel, M.2
  • 15
    • 34250231714 scopus 로고
    • Geometric quantization and multiplicities of group representations
    • [GStern]
    • [GStern] Guillemin, V. and Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math. 67, 515-538 (1982)
    • (1982) Invent. Math. , vol.67 , pp. 515-538
    • Guillemin, V.1    Sternberg, S.2
  • 16
    • 0000374308 scopus 로고
    • The Segal-Bargmann "coherent state" transform for compact Lie groups
    • [H1]
    • [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
  • 17
    • 0030672169 scopus 로고    scopus 로고
    • The inverse Segal-Bargmann transform for compact Lie groups
    • [H2]
    • [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
  • 18
    • 0031546438 scopus 로고    scopus 로고
    • Phase space bounds for quantum mechanics on a compact Lie group
    • [H3]
    • [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
  • 19
    • 0002432665 scopus 로고    scopus 로고
    • Quantum mechanics in phase space
    • [H4] Perspectives on quantization Coburn, L. and Rieffel, M., eds., Providence, R.I.: Am. Math. Soc.
    • [H4] Hall, B.: Quantum mechanics in phase space. In: Perspectives on quantization Coburn, L. and Rieffel, M., eds., Contemp. Math. Vol. 214. Providence, R.I.: Am. Math. Soc., 1998, pp. 47-62
    • (1998) Contemp. Math. , vol.214 , pp. 47-62
    • Hall, B.1
  • 20
    • 0033444082 scopus 로고    scopus 로고
    • A new form of the Segal-Bargmann transform for Lie groups of compact type
    • [H5]
    • [H5] Hall, B.: A new form of the Segal-Bargmann transform for Lie groups of compact type. Canad. J. Math. 51, 816-834 (1999)
    • (1999) Canad. J. Math. , vol.51 , pp. 816-834
    • Hall, B.1
  • 21
    • 0002501466 scopus 로고    scopus 로고
    • Holomorphic methods in analysis and mathematical physics
    • [H6]. First Summer School in Analysis and Mathematical Physics Pérez-Esteva, S. and Villegas-Blas, C. eds., Providence, R.I.: Am. Math. Soc.
    • [H6] Hall, B.: Holomorphic methods in analysis and mathematical physics. In: First Summer School in Analysis and Mathematical Physics Pérez-Esteva, S. and Villegas-Blas, C. eds., Contemp. Math. Vol. 260. Providence, R.I.: Am. Math. Soc., 2000, pp. 1-59
    • (2000) Contemp. Math. , vol.260 , pp. 1-59
    • Hall, B.1
  • 22
    • 85009761277 scopus 로고    scopus 로고
    • Harmonic analysis with respect to heat kernel measure
    • [H7]
    • [H7] Hall, B.: Harmonic analysis with respect to heat kernel measure. Bull. (N.S.) Am. Math. Soc. 38, 43-78 (2001)
    • (2001) Bull. (N.S.) Am. Math. Soc. , vol.38 , pp. 43-78
    • Hall, B.1
  • 23
    • 0035602438 scopus 로고    scopus 로고
    • Coherent states and the quantization of (1 + 1)-dimensional Yang-Mills theory
    • [H8]
    • [H8] Hall, B.: Coherent states and the quantization of (1 + 1)-dimensional Yang-Mills theory. Rev. Math. Phys. 13, 1281-1306 (2001)
    • (2001) Rev. Math. Phys. , vol.13 , pp. 1281-1306
    • Hall, B.1
  • 24
    • 0013298651 scopus 로고    scopus 로고
    • Coherent states for spheres
    • [HM], to appear. quant-ph/0109086;
    • [HM] Hall, B. and Mitchell, J.: Coherent states for spheres. J. Math. Phys., to appear. quant-ph/0109086; http://xxx.lanl.gov
    • J. Math. Phys.
    • Hall, B.1    Mitchell, J.2
  • 25
    • 0001498713 scopus 로고    scopus 로고
    • The Segal-Bargmann transform for path-groups
    • [HS]
    • [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
  • 28
    • 79551514101 scopus 로고
    • Coherent states for n-dimensional Euclidean groups E(n) and their application
    • [IK]
    • [IK] Isham, C. and Klauder, J.: Coherent states for n-dimensional Euclidean groups E(n) and their application. J. Math. Phys. 32, 607-620 (1991)
    • (1991) J. Math. Phys. , vol.32 , pp. 607-620
    • Isham, C.1    Klauder, J.2
  • 29
    • 0013248022 scopus 로고    scopus 로고
    • The ubiquitous heat kernel
    • [JL]. New York - Berlin: Springer-Verlag
    • [JL] Jorgenson, J. and Lang, S.: The ubiquitous heat kernel. In: Mathematics unlimited - 2001 and beyond. New York - Berlin: Springer-Verlag, 2001, pp. 655-683
    • (2001) Mathematics Unlimited - 2001 and Beyond , pp. 655-683
    • Jorgenson, J.1    Lang, S.2
  • 30
    • 0000097613 scopus 로고
    • Geometric quantization
    • [Ki]. Dynamical Systems IV, Arnoľd, V. and Novikov, S., eds., New York, Berlin: Springer-Verlag
    • [Ki] Kirillov, A.: Geometric quantization. In: Dynamical Systems IV, Arnoľd, V. and Novikov, S., eds., Encyclopaedia of Mathematical Sciences, Vol. 4. New York, Berlin: Springer-Verlag, 1990
    • (1990) Encyclopaedia of Mathematical Sciences , vol.4
    • Kirillov, A.1
  • 31
    • 0040195720 scopus 로고    scopus 로고
    • Quantum mechanics on a sphere and coherent states
    • [KR1]
    • [KR1] Kowalski, K. and Rembieliński, J.: Quantum mechanics on a sphere and coherent states. J. Phys. A 33, 6035-6048 (2000)
    • (2000) J. Phys. A , vol.33 , pp. 6035-6048
    • Kowalski, K.1    Rembieliński, J.2
  • 32
    • 0035537173 scopus 로고    scopus 로고
    • The Bargmann representation for the quantum mechanics on a sphere
    • [KR2]
    • [KR2] Kowalski, K. and Rembieliński, J.: The Bargmann representation for the quantum mechanics on a sphere. J. Math. Phys. 42, 4138-4147 (2001)
    • (2001) J. Math. Phys. , vol.42 , pp. 4138-4147
    • Kowalski, K.1    Rembieliński, J.2
  • 33
    • 33745057539 scopus 로고
    • Rieffel induction as generalized quantum Marsden-Weinstein reduction
    • [La1]
    • [La1] Landsman, N.: Rieffel induction as generalized quantum Marsden-Weinstein reduction. J. Geom. Phys. 15, 285-319 (1995)
    • (1995) J. Geom. Phys. , vol.15 , pp. 285-319
    • Landsman, N.1
  • 34
    • 0003313188 scopus 로고    scopus 로고
    • Mathematical topics between classical and quantum mechanics
    • [La2]. New York, Berlin: Springer-Verlag
    • [La2] Landsman, N.: Mathematical topics between classical and quantum mechanics. Springer Monographs in Mathematics. New York, Berlin: Springer-Verlag, 1998
    • (1998) Springer Monographs in Mathematics
    • Landsman, N.1
  • 35
    • 0000057368 scopus 로고
    • Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds
    • [LS]
    • [LS] Lempert, L. and Szöke, R.: Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds. Math. Ann. 290, 689-712 (1991)
    • (1991) Math. Ann. , vol.290 , pp. 689-712
    • Lempert, L.1    Szöke, R.2
  • 36
    • 4243602858 scopus 로고
    • Non-perturbative solutions for lattice quantum gravity
    • [Lo]
    • [Lo] Loll, R.: Non-perturbative solutions for lattice quantum gravity. Nucl. Phys. B 444, 619-639 (1995)
    • (1995) Nucl. Phys. B , vol.444 , pp. 619-639
    • Loll, R.1
  • 37
    • 84972571748 scopus 로고
    • Geometric quantization for the mechanics on spheres
    • [O] Mathematical Reviews, Review 83b:58038, of the paper, by Ii, K.: Tôhoku
    • [O] Onofri, E.: Mathematical Reviews, Review 83b:58038, of the paper "Geometric quantization for the mechanics on spheres," by Ii, K.: Tôhoku Math. J. 33, 289-295 (1981)
    • (1981) Math. J , vol.33 , pp. 289-295
    • Onofri, E.1
  • 38
    • 0003564717 scopus 로고
    • Generalized coherent states and their applications
    • [P]. New York, Berlin: Springer-Verlag
    • [P] Perelomov, A.: Generalized coherent states and their applications. Texts and Monographs in Physics. New York, Berlin: Springer-Verlag, 1986
    • (1986) Texts and Monographs in Physics
    • Perelomov, A.1
  • 39
    • 77957176704 scopus 로고
    • Coherent states and Kähler manifolds
    • [Ra1]
    • [Ra1] Rawnsley, J.: Coherent states and Kähler manifolds. Quart. J. Math. Oxford Sen (2) 28, 403-415 (1977)
    • (1977) Quart. J. Math. Oxford Sen (2) , vol.28 , pp. 403-415
    • Rawnsley, J.1
  • 40
    • 0000440315 scopus 로고
    • A nonunitary pairing of polarizations for the Kepler problem
    • [Ra2]
    • [Ra2] Rawnsley, J.: A nonunitary pairing of polarizations for the Kepler problem. Trans. Am. Math. Soc. 250, 167-180 (1979)
    • (1979) Trans. Am. Math. Soc. , vol.250 , pp. 167-180
    • Rawnsley, J.1
  • 41
    • 45149137712 scopus 로고
    • Quantization of Kähler manifolds. I. Geometric interpretation of Berezin's quantization
    • [RCG]
    • [RCG] Rawnsley, J., Cahen, M. and Gutt, S.: Quantization of Kähler manifolds. I. Geometric interpretation of Berezin's quantization. J. Geom. Phys. 7, 45-62 (1990)
    • (1990) J. Geom. Phys. , vol.7 , pp. 45-62
    • Rawnsley, J.1    Cahen, M.2    Gutt, S.3
  • 42
    • 0035833231 scopus 로고    scopus 로고
    • Coherent states for canonical quantum general relativity and the infinite tensor product extension
    • [STW]
    • [STW] Sahlmann, H., Thiemann, T. and Winkler, O.: Coherent states for canonical quantum general relativity and the infinite tensor product extension. Nucl. Phys. B 606, 401-440 (2001)
    • (2001) Nucl. Phys. B , vol.606 , pp. 401-440
    • Sahlmann, H.1    Thiemann, T.2    Winkler, O.3
  • 43
    • 0003272857 scopus 로고
    • Mathematical problems of relativistic physics
    • [S1], Chap. VI. Kac, M., ed., Lectures in Applied Mathematics. Providence, R.I.: Am. Math. Soc.
    • [S1] Segal, I.: Mathematical problems of relativistic physics, Chap. VI. In: Proceedings of the Summer Seminar, Boulder; Colorado, 1960, Vol. II, Kac, M., ed., Lectures in Applied Mathematics. Providence, R.I.: Am. Math. Soc., 1963
    • (1963) Proceedings of the Summer Seminar, Boulder, Colorado, 1960 , vol.2
    • Segal, I.1
  • 44
    • 84972505242 scopus 로고
    • Mathematical characterization of the physical vacuum for a linear Bose-Einstein field
    • [S2]
    • [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
  • 45
    • 0000663904 scopus 로고
    • The complex wave representation of the free boson field
    • [S3]. Topics in functional analysis: Essays dedicated to M.G. Krein on the occasion of his 70th birthday (Gohberg, I. and Kac, M., Eds). San Diego: Academic Press
    • [S3] Segal, I.: The complex wave representation of the free Boson field. In: Topics in functional analysis: Essays dedicated to M.G. Krein on the occasion of his 70th birthday (Gohberg, I. and Kac, M., Eds). Advances in Mathematics Supplementary Studies, Vol. 3. San Diego: Academic Press, 1978, pp. 321-343
    • (1978) Advances in Mathematics Supplementary Studies , vol.3 , pp. 321-343
    • Segal, I.1
  • 46
    • 0002830052 scopus 로고    scopus 로고
    • The Segal-Bargmann transform on a symmetric space of compact type
    • [St]
    • [St] Stenzel, M.: The Segal-Bargmann transform on a symmetric space of compact type. J. Funct. Anal. 165, 44-58 (1999)
    • (1999) J. Funct. Anal. , vol.165 , pp. 44-58
    • Stenzel, M.1
  • 47
    • 22244460237 scopus 로고    scopus 로고
    • Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
    • [T1]
    • [T1] Thiemann, T.: Reality conditions inducing transforms for quantum gauge field theory and quantum gravity. Classical Quantum Gravity 13, 1383-1403 (1996)
    • (1996) Classical Quantum Gravity , vol.13 , pp. 1383-1403
    • Thiemann, T.1
  • 48
    • 0032399747 scopus 로고    scopus 로고
    • Quantum spin dynamics (QSD)
    • [T2]
    • [T2] Thiemann, T.: Quantum spin dynamics (QSD). Classical Quantum Gravity 15, 839-873 (1998)
    • (1998) Classical Quantum Gravity , vol.15 , pp. 839-873
    • Thiemann, T.1
  • 49
    • 0035532879 scopus 로고    scopus 로고
    • Gauge field theory coherent states (GCS): I. General properties
    • [T3]
    • [T3] Thiemann, T.: Gauge field theory coherent states (GCS): I. General properties. Classical Quantum Gravity 18, 2025-2064 (2001)
    • (2001) Classical Quantum Gravity , vol.18 , pp. 2025-2064
    • Thiemann, T.1
  • 50
    • 0035536916 scopus 로고    scopus 로고
    • Gauge field theory coherent states (GCS): II. Peakedness properties
    • [TW1]
    • [TW1] Thiemann, T. and Winkler, O.: Gauge field theory coherent states (GCS): II. Peakedness properties. Classical Quantum Gravity 18, 2561-2636 (2001)
    • (2001) Classical Quantum Gravity , vol.18 , pp. 2561-2636
    • Thiemann, T.1    Winkler, O.2
  • 51
    • 0035540112 scopus 로고    scopus 로고
    • Gauge field theory coherent states (GCS): III. Ehrenfest theorems
    • [TW2]
    • [TW2] Thiemann, T. and Winkler, O.: Gauge field theory coherent states (GCS): III. Ehrenfest theorems. Classical Quantum Gravity 18, 4629-4681 (2001)
    • (2001) Classical Quantum Gravity , vol.18 , pp. 4629-4681
    • Thiemann, T.1    Winkler, O.2
  • 52
    • 0035604034 scopus 로고    scopus 로고
    • Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
    • [TW3]
    • [TW3] Thiemann, T. and Winkler, O.: Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit. Classical Quantum Gravity 18, 4997-5053 (2001)
    • (2001) Classical Quantum Gravity , vol.18 , pp. 4997-5053
    • Thiemann, T.1    Winkler, O.2
  • 53
    • 0003194872 scopus 로고
    • Foundations of differentiable manifolds and Lie groups
    • [Wa]. New York, Berlin: Springer-Verlag
    • [Wa] Warner, F.: Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics 94. New York, Berlin: Springer-Verlag, 1983
    • (1983) Graduate Texts in Mathematics , vol.94
    • Warner, F.1
  • 55
    • 0032558063 scopus 로고    scopus 로고
    • Constrained quantisation and θ-angles. II
    • [Wr]
    • [Wr] Wren, K.: Constrained quantisation and θ-angles. II. Nuclear Phys. B 521, 471-502 (1998)
    • (1998) Nuclear Phys. B , vol.521 , pp. 471-502
    • Wren, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.