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Volumn 195, Issue 3, 1998, Pages 549-583

Formal GNS construction and states in deformation quantization

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EID: 0032394146     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050402     Document Type: Article
Times cited : (64)

References (50)
  • 1
    • 0041138864 scopus 로고    scopus 로고
    • Representations of the Weyl group in spaces of square integrable functions with respect to p-adic valued Gaussian distributions
    • Albeverio, S., Khrennikov, A.: Representations of the Weyl group in spaces of square integrable functions with respect to p-adic valued Gaussian distributions. J. Phys. A 29, 5515-5527 (1996)
    • (1996) J. Phys. A , vol.29 , pp. 5515-5527
    • Albeverio, S.1    Khrennikov, A.2
  • 2
    • 0040131386 scopus 로고
    • Quantum group particles and non-archimedian geometry
    • Aref'eva, I. Y., Volovich, I. V.: Quantum group particles and non-archimedian geometry. Phys. Lett. B 268, 179-187 (1991)
    • (1991) Phys. Lett. B , vol.268 , pp. 179-187
    • Aref'eva, I.Y.1    Volovich, I.V.2
  • 3
    • 0001149814 scopus 로고
    • Deformation theory applied to quantization and statistical mechanics
    • Basart, H., Flato, M., Lichnerowicz, A., Sternheimer, D.: Deformation Theory applied to Quantization and Statistical Mechanics. Lett. Math. Phys. 8, 483-494 (1984)
    • (1984) Lett. Math. Phys. , vol.8 , pp. 483-494
    • Basart, H.1    Flato, M.2    Lichnerowicz, A.3    Sternheimer, D.4
  • 4
    • 0000530718 scopus 로고
    • Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions
    • Basart, H., Lichnerowicz, A.: Conformal Symplectic Geometry, Deformations, Rigidity and Geometrical (KMS) Conditions. Lett. Math. Phys. 10, 167-177 (1985)
    • (1985) Lett. Math. Phys. , vol.10 , pp. 167-177
    • Basart, H.1    Lichnerowicz, A.2
  • 7
    • 0001545426 scopus 로고
    • Quantization
    • Berezin, F.: Quantization. Izv. Mat. NAUK 38, 1109-1165 (1974)
    • (1974) Izv. Mat. NAUK , vol.38 , pp. 1109-1165
    • Berezin, F.1
  • 11
    • 0000158209 scopus 로고    scopus 로고
    • A fedosov star product of wick type for kähler manifolds
    • Bordemann, M., Waldmann, S.: A Fedosov Star Product of Wick Type for Kähler manifolds. Lett. Math. Phys. 41, 243-253 (1997)
    • (1997) Lett. Math. Phys. , vol.41 , pp. 243-253
    • Bordemann, M.1    Waldmann, S.2
  • 12
    • 0001512803 scopus 로고    scopus 로고
    • Formal GNS construction and WKB expansion in deformation quantization
    • Sternheimer, D., Rawnsley, J., Gutt, S. (eds.). Dordrecht: Kluwer
    • Bordemann, M., Waldmann, S.: Formal GNS Construction and WKB Expansion in Deformation Quantization. In: Sternheimer, D., Rawnsley, J., Gutt, S. (eds.): Deformation Theory and Symplectic Geometry. Dordrecht: Kluwer, 1997, 315-319
    • (1997) Deformation Theory and Symplectic Geometry , pp. 315-319
    • Bordemann, M.1    Waldmann, S.2
  • 14
    • 45149137712 scopus 로고
    • Quantization of kähler manifolds I
    • Cahen, M., Gutt, S., Rawnsley, J.: Quantization of Kähler Manifolds I. J. Geom. Phys. 7, 45-62 (1990)
    • (1990) J. Geom. Phys. , vol.7 , pp. 45-62
    • Cahen, M.1    Gutt, S.2    Rawnsley, J.3
  • 18
    • 0000898844 scopus 로고
    • Existence of star-products and of formal deformations of the poisson lie algebra of arbitrary symplectic manifolds
    • DeWilde, M., Lecomte, P. B. A.: Existence of star-products and of formal deformations of the Poisson Lie Algebra of arbitrary symplectic manifolds. Lett. Math. Phys. 7, 487-496 (1983)
    • (1983) Lett. Math. Phys. , vol.7 , pp. 487-496
    • DeWilde, M.1    Lecomte, P.B.A.2
  • 19
    • 0000734746 scopus 로고
    • Formal deformations of the poisson lie algebra of a symplectic manifold and star products. Existence, equivalence, derivations
    • Hazewinkel, M., Gerstenhaber, M. (eds). Dordrecht: Kluwer
    • DeWilde, M., Lecomte, P. B. A.: Formal Deformations of the Poisson Lie Algebra of a Symplectic Manifold and Star Products. Existence, Equivalence, Derivations. In: Hazewinkel, M., Gerstenhaber, M. (eds): Deformation Theory of Algebras and Structures and Applications. Dordrecht: Kluwer, 1988.
    • (1988) Deformation Theory of Algebras and Structures and Applications
    • DeWilde, M.1    Lecomte, P.B.A.2
  • 20
    • 33750947757 scopus 로고
    • The quantum structure of spacetime at the planck scale and quantum fields
    • Doplicher, S., Fredenhagen, K., Roberts, J. E.: The Quantum Structure of Spacetime at the Planck Scale and Quantum Fields. Commun. Math. Phys. 172, 187-220 (1995)
    • (1995) Commun. Math. Phys. , vol.172 , pp. 187-220
    • Doplicher, S.1    Fredenhagen, K.2    Roberts, J.E.3
  • 21
    • 84972506966 scopus 로고
    • A simple geometrical construction of deformation quantization
    • Fedosov, B.: A Simple Geometrical Construction of Deformation Quantization. J. Diff. Geom. 40, 213-238 (1994)
    • (1994) J. Diff. Geom. , vol.40 , pp. 213-238
    • Fedosov, B.1
  • 23
    • 0000668608 scopus 로고
    • Non-Archimedian strings
    • Freund, P. G. O., Oison, M.: Non-Archimedian strings. Phys. Lett. B 199, 186-190 (1987)
    • (1987) Phys. Lett. B , vol.199 , pp. 186-190
    • Freund, P.G.O.1    Oison, M.2
  • 24
    • 0001042602 scopus 로고
    • Adelic string amplitudes
    • Freund, P. G. O., Witten, E.: Adelic string amplitudes. Phys. Lett. B 199, 191-195 (1987)
    • (1987) Phys. Lett. B , vol.199 , pp. 191-195
    • Freund, P.G.O.1    Witten, E.2
  • 28
    • 0040815311 scopus 로고
    • On the definition of Hilbert space
    • Gross, H., Keller, A.: On the Definition of Hilbert Space. Manuscripta Math. 23, 67-90 (1977)
    • (1977) Manuscripta Math. , vol.23 , pp. 67-90
    • Gross, H.1    Keller, A.2
  • 30
    • 0001357629 scopus 로고
    • Quantum mechanics in phase space
    • Hansen, F.: Quantum Mechanics in Phase Space. Rep. Math. Phys. 19, 361-381 (1984)
    • (1984) Rep. Math. Phys. , vol.19 , pp. 361-381
    • Hansen, F.1
  • 33
    • 0039036761 scopus 로고
    • On p-adic Hilbert spaces
    • Kalisch, G. K.: On p-adic Hilbert Spaces. Ann. Math. 48, 180-192 (1947)
    • (1947) Ann. Math. , vol.48 , pp. 180-192
    • Kalisch, G.K.1
  • 34
    • 0039628818 scopus 로고
    • Analysis of the Moyal product in a flat space
    • Kammerer, J. B.: Analysis of the Moyal product in a flat space. J. Math. Phys. 27 (2), 529-535 (1986)
    • (1986) J. Math. Phys. , vol.27 , Issue.2 , pp. 529-535
    • Kammerer, J.B.1
  • 35
    • 0003798201 scopus 로고
    • GTM 27, New York: Springer, Reprint of the edition
    • Kelley, J. L.: General Topology. GTM 27, New York: Springer, (Reprint of the 1955 edition)
    • (1955) General Topology
    • Kelley, J.L.1
  • 36
    • 33746561894 scopus 로고
    • Ein nicht-klassischer hilbertscher raum
    • Keller, H. A.: Ein nicht-klassischer Hilbertscher Raum. Math. Z. 172, 41-49 (1980)
    • (1980) Math. Z. , vol.172 , pp. 41-49
    • Keller, H.A.1
  • 37
    • 46149135778 scopus 로고
    • On the twisted convolution product and the Weyl transformation of tempered distributions
    • Maillard, J. M.: On the twisted convolution product and the Weyl transformation of tempered distributions. J. Geom. Phys. 3, 231-261 (1986)
    • (1986) J. Geom. Phys. , vol.3 , pp. 231-261
    • Maillard, J.M.1
  • 39
    • 21844495985 scopus 로고
    • Algebraic index theorem
    • Nest, R., Tsygan, B.: Algebraic Index Theorem. Commun. Math. Phys. 172, 223-262 (1995)
    • (1995) Commun. Math. Phys. , vol.172 , pp. 223-262
    • Nest, R.1    Tsygan, B.2
  • 40
    • 0001813880 scopus 로고
    • Algebraic index theorem for families
    • Nest, R., Tsygan, B.: Algebraic Index Theorem for Families. Adv. Math. 113, 151-205 (1995)
    • (1995) Adv. Math. , vol.113 , pp. 151-205
    • Nest, R.1    Tsygan, B.2
  • 41
    • 0001454198 scopus 로고
    • Weyl manifolds and deformation quantization
    • Omori, H., Maeda, Y., Yoshioka, A.: Weyl manifolds and deformation quantization. Adv. Math. 85, 224-255 (1991)
    • (1991) Adv. Math. , vol.85 , pp. 224-255
    • Omori, H.1    Maeda, Y.2    Yoshioka, A.3
  • 42
    • 0003886677 scopus 로고
    • Ph.D. thesis, Fakultät für Mathematik der Ludwig-Maximilians-Universität, München
    • Pflaum, M. J.: Local Analysis of Deformation Quantization. Ph.D. thesis, Fakultät für Mathematik der Ludwig-Maximilians-Universität, München, 1995
    • (1995) Local Analysis of Deformation Quantization
    • Pflaum, M.J.1
  • 43
    • 77957176704 scopus 로고
    • Coherent states and kähler manifolds
    • Rawnsley, J.: Coherent States and Kähler Manifolds. Quart. J. Oxford (2), 28, 403-415 (1977)
    • (1977) Quart. J. Oxford (2) , vol.28 , pp. 403-415
    • Rawnsley, J.1
  • 44
    • 0040320056 scopus 로고
    • Algèbres associatives locales sur l'espace des sections d'un fibré en droites
    • Rubio, R.: Algèbres associatives locales sur l'espace des sections d'un fibré en droites. C.R.A.S. t.299, Série I, 699-701 (1984)
    • (1984) C.R.A.S. T.299, Série I , pp. 699-701
    • Rubio, R.1
  • 45
  • 46
  • 48
    • 0003956960 scopus 로고
    • Berlin-Heidelberg-New York: Springer-Verlag
    • v. d. Waerden: Algebra I., Berlin-Heidelberg-New York: Springer-Verlag, 1993
    • (1993) Algebra I.
    • Waerden, V.D.1
  • 49
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined on closed sets
    • Whitney, H.: Analytic extensions of differentiable functions defined on closed sets. Trans. Am. Math. Soc. 36, 63-89 (1934)
    • (1934) Trans. Am. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.