메뉴 건너뛰기




Volumn 1, Issue , 2004, Pages 54-120

Infinite Dimensional Lie Groups With Applications to Mathematical Physics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33749020978     PISSN: 13125192     EISSN: 13145673     Source Type: Journal    
DOI: 10.7546/jgsp-1-2004-54-120     Document Type: Review
Times cited : (33)

References (43)
  • 2
    • 0041796305 scopus 로고
    • A lie group structure for pseudodifferential operators
    • Adams M., Ratiu, T. and Schmid R., A lie group structure for pseudodifferential operators, Math. Ann. 273 (1986) 529-551.
    • (1986) Math. Ann. , vol.273 , pp. 529-551
    • Adams, M.1    Ratiu, T.2    Schmid, R.3
  • 3
    • 0042798593 scopus 로고
    • A lie group structure for fourier integral operators
    • Adams M., Ratiu T. and Schmid R., A lie group structure for fourier integral operators, Math. Ann. 276 (1986) 19-41.
    • (1986) Math. Ann. , vol.276 , pp. 19-41
    • Adams, M.1    Ratiu, T.2    Schmid, R.3
  • 4
    • 34250487211 scopus 로고
    • One-dimensional cohomology of lie algebras of nondivergent vector fields and rotation numbers of dynamical systems
    • Arnold V., One-dimensional cohomology of lie algebras of nondivergent vector fields and rotation numbers of dynamical systems, Funct. Anal. Appl. 3(1969)319-321.
    • (1969) Funct. Anal. Appl. , vol.3 , pp. 319-321
    • Arnold, V.1
  • 5
    • 85048670766 scopus 로고    scopus 로고
    • Banyaga A., The Structure of Classical Diffeomorphism Groups, Kluwer., Dortrecht, 1997.
    • Banyaga A., The Structure of Classical Diffeomorphism Groups, Kluwer., Dortrecht, 1997.
  • 6
    • 0542393957 scopus 로고
    • Renormalization of gauge groups
    • Becci C., Rouet A. and Stora, R., Renormalization of gauge groups, Ann. Physics 98 (1976) 287-321.
    • (1976) Ann. Physics , vol.98 , pp. 287-321
    • Becci, C.1    Rouet, A.2    Stora, R.3
  • 7
    • 85048653694 scopus 로고    scopus 로고
    • Booss B. and Bleecker, D., Topology and Analysis, Springer, New York, 1985.
    • Booss B. and Bleecker, D., Topology and Analysis, Springer, New York, 1985.
  • 8
    • 85048694498 scopus 로고    scopus 로고
    • Bourbaki N., Lie groups and lie algebras, Hermann, Paris, 1975.
    • Bourbaki N., Lie groups and lie algebras, Hermann, Paris, 1975.
  • 9
    • 0002538008 scopus 로고
    • On the group of automorphisms of a symplectic manifold
    • Princeton Univ. Press, Princeton
    • Calabi E., on the group of automorphisms of a symplectic manifold, In: Problems in Analysis, Symposium ih Honor of S. Bochner, Princeton Univ. Press, Princeton, 1970, pp.,1-26.
    • (1970) Problems in Analysis, Symposium Ih Honor of S. Bochner , pp. 1-26
    • Calabi, E.1
  • 10
    • 85048654649 scopus 로고    scopus 로고
    • Chevalley C., Theory of Lie Groups, Princeton Univ. Press, Princeton, 1946.
    • Chevalley C., Theory of Lie Groups, Princeton Univ. Press, Princeton, 1946.
  • 11
    • 84968475636 scopus 로고
    • Cohomology theory of lie groups and lie algebras
    • Chevalley C., Eilenberg S., Cohomology theory of lie groups and lie algebras, Trans. Amer. Math. Soc. 63 (1948) 85-124.
    • (1948) Trans. Amer. Math. Soc. , vol.63 , pp. 85-124
    • Chevalley, C.1    Eilenberg, S.2
  • 12
    • 0005859448 scopus 로고    scopus 로고
    • Quantum field theory and strings: A course for mathematicians
    • Providence
    • Deligne P et al. (Eds), Quantum field theory and strings: a course for mathematicians, Vols. 1 and 2, Amer. Math. Soc, Providence, 1999.
    • (1999) Amer. Math. Soc , vol.1-2
    • Deligne, P.1
  • 13
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of In-compressible fluid
    • Ebin D. and Marsden J., Groups of diffeomorphisms and the motion of In-compressible fluid, Ann. of Math. 92 (1970) 102-163.
    • (1970) Ann. of Math. , vol.92 , pp. 102-163
    • Ebin, D.1    Marsden, J.2
  • 14
    • 0000950801 scopus 로고
    • The manifold structure of maps between open manifolds
    • Eichhorn J., The manifold structure of maps between open manifolds, Ann. Global Anal. Geom. 11 (1993) 253-300.
    • (1993) Ann. Global Anal. Geom. , vol.11 , pp. 253-300
    • Eichhorn, J.1
  • 15
    • 0042297486 scopus 로고    scopus 로고
    • Form preserving diffeomorphisms on open manifolds
    • Eichhorn J. and Schmid, R., Form Preserving Diffeomorphism Groups on Open Manifolds, Ann. Global Anal. Geom. 14 (1996) 147-176. (Pubitemid 126716636)
    • (1996) Annals of Global Analysis and Geometry , vol.14 , Issue.2 , pp. 147-176
    • Eichhorn, J.1    Schmid, R.2
  • 16
    • 0042407829 scopus 로고    scopus 로고
    • Lie groups of Fourier integral operators on open manifolds
    • Eichhorn J. and Schmid R., Lie Groups of Fourier Integral Operators on Open Manifolds, Comm. Analysis and Geometry 9 (2001) 983-1040. (Pubitemid 33614355)
    • (2001) Communications in Analysis and Geometry , vol.9 , Issue.5 , pp. 983-1040
    • Eichhorn, J.1    Schmid, R.2
  • 17
    • 85048687233 scopus 로고    scopus 로고
    • Eichhorn J. and Schmid R., Applications of the Lie Group of Fourier Integral Operators to Fluid Dynamics, Preprint, 2003.
    • Eichhorn J. and Schmid R., Applications of the Lie Group of Fourier Integral Operators to Fluid Dynamics, Preprint, 2003.
  • 18
    • 0041712037 scopus 로고
    • The diffeomorphism group approach to nonlinear quantum systems
    • Goldin G., The diffeomorphism group approach to nonlinear quantum systems. Int. J. Mod. Physics B 6 (1992) 1905-1916.
    • (1992) Int. J. Mod. Physics B , vol.6 , pp. 1905-1916
    • Goldin, G.1
  • 19
    • 4243314759 scopus 로고
    • Diffeomorphism groups, gauge groups, and quantum theory
    • Goldin G., Menikoff R. and Sharp D., Diffeomorphism groups, gauge groups, and quantum theory. Phys. Rev. Lett. 51 (1983) 2246-2249.
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 2246-2249
    • Goldin, G.1    Menikoff, R.2    Sharp, D.3
  • 20
    • 84966236065 scopus 로고
    • The inverse function theorem of nash and moser
    • Hamilton R., The inverse function theorem of nash and moser, Bull. Amer. Math. Soc. 7 (1982) 65-222.
    • (1982) Bull. Amer. Math. Soc. , vol.7 , pp. 65-222
    • Hamilton, R.1
  • 22
    • 0002535842 scopus 로고
    • Quantization and unitary representations, lectures in modern analysis and applications III
    • Kostant B., Quantization and unitary representations, lectures in modern analysis and applications III, Lecture Notes in Math. Vol. 170 (1970) 87208.
    • (1970) Lecture Notes in Math. , vol.170 , pp. 87208
    • Kostant, B.1
  • 23
    • 0000876641 scopus 로고
    • The solution to a generalized toda lattice and representation theory
    • Kostant B., The solution to a generalized toda lattice and representation theory, Adv. Math. 34 (1979) 195-338.
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Kostant, B.1
  • 24
    • 85048670672 scopus 로고    scopus 로고
    • Lang S., Introduction to Differentiable Manifolds, John Wiley, New York, 1962.
    • Lang S., Introduction to Differentiable Manifolds, John Wiley, New York, 1962.
  • 26
    • 0000388192 scopus 로고
    • A rapidly convergent iteration method and non-linear differential equations
    • Moser J., A rapidly convergent iteration method and non-linear differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 20 (1966) 499-535.
    • (1966) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.20 , pp. 499-535
    • Moser, J.1
  • 27
    • 0002702476 scopus 로고
    • The embedding problem for riemannian manifolds
    • Nash J., The embedding problem for riemannian manifolds, Ann. of Math. 63 (1956) 20-63.
    • (1956) Ann. of Math. , vol.63 , pp. 20-63
    • Nash, J.1
  • 29
    • 0008059961 scopus 로고    scopus 로고
    • Infinite-dimensional lie groups
    • Amer. Math. Soc, Providence
    • Omori H., Infinite-Dimensional Lie Groups, Transi. Math. Monographs Vol. 158,Amer. Math. Soc, Providence, 1996.
    • (1996) Transi. Math. Monographs , vol.58
    • Omori, H.1
  • 30
    • 85048693777 scopus 로고    scopus 로고
    • Palais R., Foundations of Global Nonlinear Analysis, Addison-Wesley, Reading, 1968.
    • Palais R., Foundations of Global Nonlinear Analysis, Addison-Wesley, Reading, 1968.
  • 31
    • 85048674328 scopus 로고    scopus 로고
    • Pressley A. and Segal G., Loop Groups, Oxford Univ. Press, Oxford, 1986.
    • Pressley A. and Segal G., Loop Groups, Oxford Univ. Press, Oxford, 1986.
  • 32
    • 0002407238 scopus 로고
    • The differential structure of three remarkable diffeomorphism Groups
    • Ratiu T. and Schmid R., The differential structure of three remarkable diffeomorphism Groups, Math. Z. 177 (1981) 81-100.
    • (1981) Math. Z. , vol.177 , pp. 81-100
    • Ratiu, T.1    Schmid, R.2
  • 33
    • 85048658440 scopus 로고    scopus 로고
    • Schmid R., Die Symplektomorphismen-Gruppe als Frechet Lie Gruppe, PhD Thesis, Juris Druck + Verlag, Zuerich, 1978.
    • Schmid R., Die Symplektomorphismen-Gruppe als Frechet Lie Gruppe, PhD Thesis, Juris Druck + Verlag, Zuerich, 1978.
  • 34
    • 84888199785 scopus 로고
    • The inverse function theorem of nash and moser for the tdifferentiability
    • Schmid R., The inverse function theorem of nash and moser for the tdifferentiability, Abh. Akad. Wiss. Berlin 1984-2N (1984) 201-206.
    • (1984) Abh. Akad. Wiss. Berlin , vol.1984-2N , pp. 201-206
    • Schmid, R.1
  • 35
    • 85048664989 scopus 로고    scopus 로고
    • Schmid R.,Infinite dimensional hamiltonian systems, monographs and textbooks in physical sciences, Biblionopolis, Napoli, 1987.
    • Schmid R.,Infinite dimensional hamiltonian systems, monographs and textbooks in physical sciences, Biblionopolis, Napoli, 1987.
  • 36
    • 84972565989 scopus 로고
    • The geometry of BRS transformations
    • Schmid R., The geometry of BRS transformations, Illinois J. Math., 34 (1990)87-97.
    • (1990) Illinois J. Math. , vol.34 , pp. 87-97
    • Schmid, R.1
  • 37
    • 84872936079 scopus 로고
    • Diffeomorphism groups, pseudodifferential operators and rMatrices
    • D. Ferrus Lecture Notes in Math.
    • Schmid R., Diffeomorphism groups, pseudodifferential operators and rMatrices, In: Global Differential Geometry, D. Ferrus et al (Eds), Lecture Notes in Math. Vol. 1481 (1991) 258-263.
    • (1991) Global Differential Geometry , vol.1481 , pp. 258-263
    • Schmid, R.1
  • 38
    • 43949148263 scopus 로고
    • Local cohomology in gauge theories, BRST Transformations and Anomalies
    • Schmid R., Local cohomology in gauge theories, BRST Transformations and Anomalies, Differential Geom. Appl. 4 (1994) 107-116.
    • (1994) Differential Geom. Appl. , vol.4 , pp. 107-116
    • Schmid, R.1
  • 39
    • 84872898466 scopus 로고    scopus 로고
    • Q-symplectic orbits and a solution of the BRST consistency condition
    • I. Mladenov and G. Naber (Eds), Coral Press, Sofia
    • Schmid R., Q-symplectic orbits and a solution of the BRST consistency condition, In: Geometry, Integrability and Quantization IV, I. Mladenov and G. Naber (Eds), Coral Press, Sofia 2003, 284-295.
    • (2003) Geometry, Integrability and Quantization IV , pp. 284-295
    • Schmid, R.1
  • 40
    • 84978228084 scopus 로고
    • Hamiltonian group actions and integrable systems
    • Symes W., Hamiltonian group actions and integrable systems, Physica D 1 (1980)339-374.
    • (1980) Physica D , vol.1 , pp. 339-374
    • Symes, W.1
  • 41
    • 84912598412 scopus 로고
    • Gauge invariance in field theory and statistical mechanics
    • unpublished.
    • Tyutin I., Gauge invariance in field theory and statistical mechanics, Lebedev Inst. Preprint 39, 1976, unpublished.
    • (1976) Lebedev Inst. Preprint , vol.39
    • Tyutin, I.1
  • 42
    • 85048678344 scopus 로고    scopus 로고
    • Varadarajan V., Lie Groups, Lie Algebras, and their Representations, Prentice-Hall, Inc., Englewood Cliffs, 1974.
    • Varadarajan V., Lie Groups, Lie Algebras, and their Representations, Prentice-Hall, Inc., Englewood Cliffs, 1974.
  • 43
    • 0000595516 scopus 로고
    • Symplectic manifolds and their lagrangian submanifolds
    • Weinstein A., Symplectic manifolds and their lagrangian submanifolds, Adv. Math. 6 (1971) 329-346.
    • (1971) Adv. Math. , vol.6 , pp. 329-346
    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.