메뉴 건너뛰기




Volumn 33, Issue 8-9, 2010, Pages 401-590

From the equations of motion to the canonical commutation relations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 78651501301     PISSN: 0393697X     EISSN: None     Source Type: Journal    
DOI: 10.1393/ncr/i2010-10057-x     Document Type: Article
Times cited : (58)

References (243)
  • 7
    • 51649178485 scopus 로고
    • Group-theoretical analysis of elementary particles in an external electromagnetic field
    • BACRY H., Group-Theoretical Analysis of Elementary Particles in an External Electromagnetic Field, Nuovo Cimento A, 70 (1970) 289.
    • (1970) Nuovo Cimento A , vol.70 , pp. 289
    • Bacry, H.1
  • 10
    • 78651499826 scopus 로고
    • A lagrangian approach to the no-interaction theorem
    • BALACHANDRAN A. P., MARMO G. and STERN A., A Lagrangian Approach to the No-Interaction Theorem, Nuovo Cimento A, 11 (1982) 69.
    • (1982) Nuovo Cimento A , vol.11 , pp. 69
    • Balachandran, A.P.1    Marmo, G.2    Stern, A.3
  • 11
    • 0001999817 scopus 로고
    • On unitary ray representations of continuous groups
    • BARGMANN V., On Unitary Ray Representations of Continuous Groups, Ann. Math., 59 (1954) 1.
    • (1954) Ann. Math. , vol.59 , pp. 1
    • Bargmann, V.1
  • 12
  • 13
    • 0000530718 scopus 로고
    • Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions
    • BASART H. and LICHNEROWICZ A., Conformal Symplectic Geometry, Deformations, Rigidity and Geometrical (KMS) Conditions, Lett. Math. Phys., 10 (1985) 167.
    • (1985) Lett. Math. Phys. , vol.10 , pp. 167
    • Basart, H.1    Lichnerowicz, A.2
  • 14
    • 0035916038 scopus 로고    scopus 로고
    • Non-hermitian oscillator-like hamiltonians and λ-coherent states revisited
    • BECKERS J., DEBERGH N., CARIÑENA J. F. and MARMO G., Non-Hermitian Oscillator-Like Hamiltonians and Λ-Coherent States Revisited, Mod. Phys. Lett. A, 16 (2001) 91.
    • (2001) Mod. Phys. Lett. A , vol.16 , pp. 91
    • Beckers, J.1    Debergh, N.2    Cariñena, J.F.3    Marmo, G.4
  • 15
    • 34547309949 scopus 로고    scopus 로고
    • Making sense of non-hermitian hamiltonians
    • BENDER C. M., Making Sense of Non-Hermitian Hamiltonians, Rep. Prog. Phys., 70 (2007) 947.
    • (2007) Rep. Prog. Phys. , vol.70 , pp. 947
    • Bender, C.M.1
  • 16
    • 0036848830 scopus 로고    scopus 로고
    • Remarks on the connection between the additive separation of the Hamilton-Jacobi equation and the multiplicative separability of the schrödinger equation. I. The completeness and robertson condition
    • BENENTI S., CHANU C. and RASTELLI G., Remarks on the Connection Between the Additive Separation of the Hamilton-Jacobi Equation and the Multiplicative Separability of the Schrödinger Equation. I. The Completeness and Robertson Condition, J. Math. Phys., 43 (2002) 5183.
    • (2002) J. Math. Phys. , vol.43 , pp. 5183
    • Benenti, S.1    Chanu, C.2    Rastelli, G.3
  • 17
    • 0036851032 scopus 로고    scopus 로고
    • Remarks on the connection between the additive separation of the Hamilton-Jacobi equation and the multiplicative separability of the schrödinger equation. II. First integrals and symmetry operators
    • BENENTI S., CHANU C. and RASTELLI G., Remarks on the Connection Between the Additive Separation of the Hamilton-Jacobi Equation and the Multiplicative Separability of the Schrödinger Equation. II. First Integrals and Symmetry Operators, J. Math. Phys., 43 (2002) 5223.
    • (2002) J. Math. Phys. , vol.43 , pp. 5223
    • Benenti, S.1    Chanu, C.2    Rastelli, G.3
  • 18
    • 17444424268 scopus 로고    scopus 로고
    • Variable separation theory for the null Hamilton-Jacobi equation
    • BENENTI S., CHANU C. and RASTELLI G., Variable Separation Theory for the Null Hamilton-Jacobi Equation, J. Math. Phys., 46 (2005) 042901.
    • (2005) J. Math. Phys. , vol.46 , pp. 042901
    • Benenti, S.1    Chanu, C.2    Rastelli, G.3
  • 24
    • 0041177178 scopus 로고
    • Linear fields according to I. E. Segal
    • edited by Streater R. F. Academic Press, New York
    • BONGAARTS P. J. M., Linear Fields According to I. E. Segal, in Mathematics of Contemporary Physics, edited by Streater R. F. (Academic Press, New York) 1972.
    • (1972) Mathematics of Contemporary Physics
    • Bongaarts, P.J.M.1
  • 25
    • 51249192918 scopus 로고
    • "Ambiguities" of harmonic-oscillator commutation relations
    • BOULWARE D. G. and DESER S., "Ambiguities" of Harmonic-Oscillator Commutation Relations, Nuovo Cimento, XXX (1963) 230.
    • (1963) Nuovo Cimento , vol.30 , pp. 230
    • Boulware, D.G.1    Deser, S.2
  • 28
    • 36149027030 scopus 로고
    • Bloch electrons in a uniform magnetic field
    • BROWN E., Bloch Electrons in a Uniform Magnetic Field, Phys. Rev. A, 133 (1964) 1038.
    • (1964) Phys. Rev. A , vol.133 , pp. 1038
    • Brown, E.1
  • 29
    • 78651494170 scopus 로고    scopus 로고
    • Editor, World Scientific, Singapore
    • BROWN L. M. (Editor), Feynman's Thesis (World Scientific, Singapore) 2005.
    • (2005) Feynman's Thesis
    • Brown, L.M.1
  • 30
    • 4544250525 scopus 로고    scopus 로고
    • On the quantization of newton-equivalent hamiltonians
    • CALOGERO F. and DE GASPERIS A., On the Quantization of Newton-Equivalent Hamiltonians, Am. J. Phys., 9 (2004) 1202.
    • (2004) Am. J. Phys. , vol.9 , pp. 1202
    • Calogero, F.1    De Gasperis, A.2
  • 34
    • 18044402148 scopus 로고    scopus 로고
    • Contractions nijenhuis tensors for general algebraic structures
    • CARIÑENA J. F., GRABOWSKI J. and MARMO G., Contractions Nijenhuis Tensors for General Algebraic Structures, J. Phys. A, 34 (2001) 3769.
    • (2001) J. Phys. A , vol.34 , pp. 3769
    • Cariñena, J.F.1    Grabowski, J.2    Marmo, G.3
  • 35
    • 0010068413 scopus 로고
    • The feynman problem and the inverse problem for poisson dynamics
    • CARIÑENA J. F., IBORT L. A., MARMO G. and STERN A., The Feynman Problem and the Inverse Problem for Poisson Dynamics, Phys. Rep., 263 (1995) 153.
    • (1995) Phys. Rep. , vol.263 , pp. 153
    • Cariñena, J.F.1    Ibort, L.A.2    Marmo, G.3    Stern, A.4
  • 36
    • 0037195737 scopus 로고    scopus 로고
    • Non-symplectic symmetries and Bi-hamiltonian structures for the rational harmonic oscillator
    • CARIÑENA J. F., MARMO G. and RAÑADA M. F., Non-Symplectic Symmetries and Bi-Hamiltonian Structures for the Rational Harmonic Oscillator, J. Phys. A, 35 (2002) L679.
    • (2002) J. Phys. A , vol.35
    • Cariñena, J.F.1    Marmo, G.2    Rañada, M.F.3
  • 37
    • 0041708506 scopus 로고    scopus 로고
    • A generalization of the stone-von neumann theorem of non-regular representation of the CCR algebra
    • CAVALLARO S., MORCHIO G. and STROCCHI F., A Generalization of the Stone-von Neumann Theorem of Non-Regular Representation of the CCR Algebra, Lett. Math. Phys., 47 (1999) 307.
    • (1999) Lett. Math. Phys. , vol.47 , pp. 307
    • Cavallaro, S.1    Morchio, G.2    Strocchi, F.3
  • 39
    • 31344442837 scopus 로고    scopus 로고
    • Wigner-weyl correspondence in quantum mechanics for continuous and discrete systems. A dirac-inspired view
    • CHATURVEDI S., ERCOLESSI E., MARMO G., MORANDI G., MUKUNDA N. and SIMON R., Wigner-Weyl Correspondence in Quantum Mechanics for Continuous and Discrete Systems. A Dirac-inspired View, J. Phys. A, 39 (2006) 1405.
    • (2006) J. Phys. A , vol.39 , pp. 1405
    • Chaturvedi, S.1    Ercolessi, E.2    Marmo, G.3    Morandi, G.4    Mukunda, N.5    Simon, R.6
  • 42
    • 78049315528 scopus 로고    scopus 로고
    • Remarks on the GNS representation and the geometry of quantum states
    • CHRUŚHINSKI D. and MARMO G., Remarks on the GNS Representation and the Geometry of Quantum States, Open Syst. Inf. Dyn., 16 (2009) 157.
    • (2009) Open Syst. Inf. Dyn. , vol.16 , pp. 157
    • Chruśhinski, D.1    Marmo, G.2
  • 44
    • 78651470608 scopus 로고    scopus 로고
    • The space of density states in geometrical quantum mechanics
    • edited by Cantrijn F., Crampin M. and Langerock B. Gent Academia Press, Gent
    • CLEMENTE-GALLARDO J. and MARMO G., The Space of Density States in Geometrical Quantum Mechanics, in Differential Geometric Methods in Mechanics and Field Theory, edited by Cantrijn F., Crampin M. and Langerock B. (Gent Academia Press, Gent) 2007.
    • (2007) Differential Geometric Methods in Mechanics and Field Theory
    • Clemente-Gallardo, J.1    Marmo, G.2
  • 45
    • 0001475402 scopus 로고
    • The mathematics of second quantization
    • COOK J. M., The Mathematics of Second Quantization, Trans. Am. Math. Soc., 74 (1953) 222.
    • (1953) Trans. Am. Math. Soc. , vol.74 , pp. 222
    • Cook, J.M.1
  • 46
    • 36149019582 scopus 로고
    • Relativistic invariance and hamiltonian theories of interacting particles
    • CURRIE D. G., JORDAN T. F. and SUDARSHAN E. C. G., Relativistic Invariance and Hamiltonian Theories of Interacting Particles, Rev. Mod. Phys., 35 (1963) 350.
    • (1963) Rev. Mod. Phys. , vol.35 , pp. 350
    • Currie, D.G.1    Jordan, T.F.2    Sudarshan, E.C.G.3
  • 47
    • 0000525364 scopus 로고
    • Q-equivalent particle hamiltonians. I. The classical one-dimensional case
    • CURRIE D. G. and SALETAN E. J., q-Equivalent Particle Hamiltonians. I. The Classical One-Dimensional Case, J. Math. Phys., 7 (1966) 967.
    • (1966) J. Math. Phys. , vol.7 , pp. 967
    • Currie, D.G.1    Saletan, E.J.2
  • 48
    • 51649186164 scopus 로고
    • Canonical transformations and quadratic hamiltonians
    • CURRIE D. G. and SALETAN E. J., Canonical Transformations and Quadratic Hamiltonians, Nuovo Cimento B, 9 (1972) 143.
    • (1972) Nuovo Cimento B. , vol.9 , pp. 143
    • Currie, D.G.1    Saletan, E.J.2
  • 49
    • 0001455649 scopus 로고
    • Adams representation and localization in a magnetic field
    • DANA I. and ZAK J., Adams Representation and Localization in a Magnetic Field, Phys. Rev. B, 28 (1983) 694.
    • (1983) Phys. Rev. B. , vol.28 , pp. 694
    • Dana, I.1    Zak, J.2
  • 50
    • 0004225382 scopus 로고
    • World Scientific, Singapore
    • DAS A., Integrable Models (World Scientific, Singapore) 1989.
    • (1989) Integrable Models
    • Das, A.1
  • 57
    • 0001888324 scopus 로고
    • The lagrangian in quantum mehanics
    • DIRAC P. A. M., The Lagrangian in Quantum Mehanics, Phys. Z. Sowjetunion, 3, Issue No. 1 (1933) 64.
    • (1933) Phys. Z. Sowjetunion , vol.3 , Issue.1 , pp. 64
    • Dirac, P.A.M.1
  • 58
    • 84942830232 scopus 로고
    • Solution of the inverse problem of the calculus of variations
    • DOUGLAS J., Solution of the Inverse Problem of the Calculus of Variations, Trans. Am. Math. Soc., 50 (1941) 71.
    • (1941) Trans. Am. Math. Soc. , vol.50 , pp. 71
    • Douglas, J.1
  • 61
    • 0000864421 scopus 로고
    • Alternative hamiltonian descriptions for quantum systems
    • DUBROVIN B. A., MARMO G. and SIMONI A., Alternative Hamiltonian Descriptions for Quantum Systems, Mod. Phys. Lett. A, 5 (1990) 1229.
    • (1990) Mod. Phys. Lett. A , vol.5 , pp. 1229
    • Dubrovin, B.A.1    Marmo, G.2    Simoni, A.3
  • 62
    • 0001225877 scopus 로고
    • Ground states of a two-dimensional electron in a periodic potential
    • DUBROVIN B. A. and NOVIKOV S. P., Ground States of a Two-Dimensional Electron in a Periodic Potential, Sov. Phys. JETP, 52 (1980) 511.
    • (1980) Sov. Phys. JETP , vol.52 , pp. 511
    • Dubrovin, B.A.1    Novikov, S.P.2
  • 63
    • 0001187280 scopus 로고
    • Feynman's proof of the maxwell equations
    • DYSON F. J., Feynman's Proof of the Maxwell Equations, Am. J. Phys., 58 (1990) 209.
    • (1990) Am. J. Phys. , vol.58 , pp. 209
    • Dyson, F.J.1
  • 66
    • 34547585113 scopus 로고    scopus 로고
    • Alternative linear structures for classical and quantum systems
    • ERCOLESSI E., IBORT L. A., MARMO G. and MORANDI G., Alternative Linear Structures for Classical and Quantum Systems, Int. J. Mod. Phys. A, 22 (2007) 3039.
    • (2007) Int. J. Mod. Phys. A , vol.22 , pp. 3039
    • Ercolessi, E.1    Ibort, L.A.2    Marmo, G.3    Morandi, G.4
  • 67
    • 0037145384 scopus 로고    scopus 로고
    • Alternative hamiltonian descriptions and statistical mechanics
    • ERCOLESSI E., MARMO G. and MORANDI G., Alternative Hamiltonian Descriptions and Statistical Mechanics, Int. J. Mod. Phys. A, 17 (2002) 3779.
    • (2002) Int. J. Mod. Phys. A , vol.17 , pp. 3779
    • Ercolessi, E.1    Marmo, G.2    Morandi, G.3
  • 71
    • 0001965116 scopus 로고
    • Description of states in quantum mechanics by density matrix and operator techniques
    • FANO U., Description of States in Quantum Mechanics by Density Matrix and Operator Techniques, Rev. Mod. Phys., 29 (1957) 74.
    • (1957) Rev. Mod. Phys. , vol.29 , pp. 74
    • Fano, U.1
  • 72
    • 33744730406 scopus 로고
    • Separability of completely-integrable dynamical systems admitting alternative lagrangian descriptions
    • FERRARIO C., LOVECCHIO G., MARMO G., MORANDI G. and RUBANO C., Separability of Completely-Integrable Dynamical Systems Admitting Alternative Lagrangian Descriptions, Lett. Math. Phys., 9 (1985) 140.
    • (1985) Lett. Math. Phys. , vol.9 , pp. 140
    • Ferrario, C.1    Lovecchio, G.2    Marmo, G.3    Morandi, G.4    Rubano, C.5
  • 73
    • 25444451137 scopus 로고
    • A separability theorem for dynamical systems admitting alternative lagrangian descriptions
    • FERRARIO C., LOVECCHIO G., MARMO G., MORANDI G. and RUBANO C., A Separability Theorem for Dynamical Systems Admitting Alternative Lagrangian Descriptions, J. Phys. A, 20 (1987) 3225.
    • (1987) J. Phys. A , vol.20 , pp. 3225
    • Ferrario, C.1    Lovecchio, G.2    Marmo, G.3    Morandi, G.4    Rubano, C.5
  • 74
    • 34547361024 scopus 로고
    • Space-time approach to non-relativistic quantum mechanics
    • FEYNMAN R. P., Space-Time Approach to Non-Relativistic Quantum Mechanics, Rev. Mod. Phys., 20 (1948) 367.
    • (1948) Rev. Mod. Phys. , vol.20 , pp. 367
    • Feynman, R.P.1
  • 76
    • 0030268742 scopus 로고    scopus 로고
    • Magnetic translation groups in n dimensions
    • FLOREK W., Magnetic Translation Groups in n Dimensions, Rep. Math. Phys., 38 (1996) 235.
    • (1996) Rep. Math. Phys. , vol.38 , pp. 235
    • Florek, W.1
  • 78
    • 0000793354 scopus 로고
    • Theory of vector-valued differential forms
    • FROLICHER A. and NIJENHUIS A., Theory of Vector-Valued Differential Forms, Indag. Math., 18 (1956) 338.
    • (1956) Indag. Math. , vol.18 , pp. 338
    • Frolicher, A.1    Nijenhuis, A.2
  • 79
    • 51649202645 scopus 로고
    • Some myriotic paraboson fields
    • GALINDO A., Some Myriotic Paraboson Fields, Nuovo Cimento, XXX (1963) 235.
    • (1963) Nuovo Cimento , vol.30 , pp. 235
    • Galindo, A.1
  • 80
    • 33745701144 scopus 로고
    • The schouten bracket and hamiltonian operators
    • GEL'FAND I. M. and DORFMAN I. YA., The Schouten Bracket and Hamiltonian Operators, Funct. Anal. Appl., 14 (1981) 223.
    • (1981) Funct. Anal. Appl. , vol.14 , pp. 223
    • Gel'Fand, I.M.1    Dorfman, I.Ya.2
  • 81
    • 0002700949 scopus 로고
    • On local geometry of a bihamiltonian structure
    • edited by Corwin L., Gel'fand I. M. and Lepowski J., Birkhauser, Boston
    • GEL'FAND I. M. and ZAKHAREVICH I., On Local geometry of a Bihamiltonian Structure, in Gel'fand Mathematical Seminars Series, edited by Corwin L., Gel'fand I. M. and Lepowski J., Vol. I (Birkhauser, Boston) 1993.
    • (1993) Gel'fand Mathematical Seminars Series , vol.1
    • Gel'Fand, I.M.1    Zakharevich, I.2
  • 82
    • 0004293978 scopus 로고
    • University of Chicago Press, Chicago
    • GEROCH R., Mathematical Physics (University of Chicago Press, Chicago) 1985.
    • (1985) Mathematical Physics
    • Geroch, R.1
  • 83
    • 0000065234 scopus 로고
    • The inverse problem in the hamiltonian formalism integrability of linear vector fields
    • GIORDANO M., MARMO G. and RUBANO C., The Inverse Problem in the Hamiltonian Formalism Integrability of Linear Vector Fields, Inverse Problems, 9 (1993) 443.
    • (1993) Inverse Problems , vol.9 , pp. 443
    • Giordano, M.1    Marmo, G.2    Rubano, C.3
  • 84
    • 3142549017 scopus 로고    scopus 로고
    • Integrable and super-integrable systems in classical and quantum mechanics
    • edited by Ablowitz M. J., Boiti M., Pempinelli F. and Prinari B., World Scientific, Singapore
    • GIORDANO M., MARMO G., SIMONI A. and VENTRIGLIA F., Integrable and Super-Integrable Systems in Classical and Quantum Mechanics, in Nonlinear Physics Theory and Experiment, edited by Ablowitz M. J., Boiti M., Pempinelli F. and Prinari B., Vol. II (World Scientific, Singapore) 2003.
    • (2003) Nonlinear Physics Theory and Experiment , vol.2
    • Giordano, M.1    Marmo, G.2    Simoni, A.3    Ventriglia, F.4
  • 86
    • 27844514662 scopus 로고    scopus 로고
    • Geometry of quantum systems density states and entanglement
    • GRABOWSKI J., KUS M. and MARMO G., Geometry of Quantum Systems Density States and Entanglement, J. Phys. A, 38 (2005) 10127.
    • (2005) J. Phys. A , vol.38 , pp. 10127
    • Grabowski, J.1    Kus, M.2    Marmo, G.3
  • 87
    • 70449572384 scopus 로고    scopus 로고
    • Wigner's theorem and the geometry of extreme positive maps
    • GRABOWSKI J., KUS M. and MARMO G., Wigner's Theorem and the Geometry of Extreme Positive Maps, J. Phys. A, 42 (2009) 345301.
    • (2009) J. Phys. A , vol.42 , pp. 345301
    • Grabowski, J.1    Kus, M.2    Marmo, G.3
  • 89
    • 23944439976 scopus 로고    scopus 로고
    • Binary operations in classical and quantum mechanics
    • edited by Grabowski J. and Urbanski P., Banach Center Publ.
    • GRABOWSKI J. and MARMO G., Binary Operations in Classical and Quantum Mechanics, in Classical and Quantum Integrability, edited by Grabowski J. and Urbanski P., Vol. 59 (Banach Center Publ.) 2003, p. 163.
    • (2003) Classical and Quantum. Integrability , vol.59 , pp. 163
    • Grabowski, J.1    Marmo, G.2
  • 91
    • 36149019104 scopus 로고
    • A generalized method of field quantization
    • GREEN H. S., A Generalized Method of Field Quantization, Phys. Rev., 90 (1953) 270.
    • (1953) Phys. Rev. , vol.90 , pp. 270
    • Green, H.S.1
  • 92
    • 0347851767 scopus 로고
    • Selection rules for parafields and the absence of para particles in nature
    • GREENBERG O. W. and MESSIAH A. M. L., Selection Rules for Parafields and the Absence of Para Particles in Nature, Phys. Rev. B, 138 (1965) B1155.
    • (1965) Phys. Rev. B. , vol.138
    • Greenberg, O.W.1    Messiah, A.M.L.2
  • 93
    • 33745040449 scopus 로고
    • On the principles of elementary quantum mechanics
    • GROENEWOLD A., On the Principles of Elementary Quantum Mechanics, Physica, 12 (1946) 405.
    • (1946) Physica , vol.12 , pp. 405
    • Groenewold, A.1
  • 94
    • 0000631775 scopus 로고
    • An algebra of pseudo-differential operators and quantum mechanics in phase space
    • GROSSMANN A., LOUPIAS G. and STEIN E. M., An Algebra of Pseudo-Differential Operators and Quantum Mechanics in Phase Space, Ann. Inst. Fourier, Grenoble, 18 (1968) 2343.
    • (1968) Ann. Inst. Fourier, Grenoble , vol.18 , pp. 2343
    • Grossmann, A.1    Loupias, G.2    Stein, E.M.3
  • 96
    • 34250536977 scopus 로고
    • On the equilibrium states in quantum statistical mechanics
    • HAAG R., HUGENHOLTZ N. M. and WINNINK M., On the Equilibrium States in Quantum Statistical Mechanics, Commun. Math. Phys., 5 (1967) 215.
    • (1967) Commun. Math. Phys. , vol.5 , pp. 215
    • Haag, R.1    Hugenholtz, N.M.2    Winnink, M.3
  • 97
    • 6144286355 scopus 로고
    • An algebaric approach to quantum field theory
    • HAAG R. and KASTLER D., An Algebaric Approach to Quantum Field Theory, J. Math. Phys., 5 (1964) 884.
    • (1964) J. Math. Phys. , vol.5 , pp. 884
    • Haag, R.1    Kastler, D.2
  • 98
    • 51249193431 scopus 로고
    • The range of application of the lagrangian formalism
    • HAVA S O., The Range of Application of the Lagrangian Formalism, Suppl. Nuovo Cimento, 3 (1957) 363.
    • (1957) Suppl. Nuovo Cimento , vol.3 , pp. 363
    • Hava, S.O.1
  • 99
    • 0009147074 scopus 로고
    • Ueber die phisikalische bedeutung des prinzip der klenisten wirkung
    • HELMOLTZ H., Ueber die Phisikalische Bedeutung des Prinzip der Klenisten Wirkung, Z. Reine Angew. Math., 100 (1887) 137.
    • (1887) Z. Reine Angew. Math. , vol.100 , pp. 137
    • Helmoltz, H.1
  • 100
    • 36749107317 scopus 로고
    • Lagrangians for spherically symmetric potentials
    • HENNEAUX M. and SHEPLEY L. C., Lagrangians for Spherically Symmetric Potentials, J. Math. Phys., 23 (1982) 2101.
    • (1982) J. Math. Phys. , vol.23 , pp. 2101
    • Henneaux, M.1    Shepley, L.C.2
  • 101
    • 0002995775 scopus 로고
    • On the cohomology theory for associative algebras
    • HOCHSCHILD G., On the Cohomology Theory for Associative Algebras, Ann. Math., 47 (1946) 568.
    • (1946) Ann. Math. , vol.47 , pp. 568
    • Hochschild, G.1
  • 102
    • 0001032458 scopus 로고
    • Energy levels and wavefunctions of bloch electrons in rational and irrational magnetic fields
    • HOFSTADTER D. R., Energy Levels and Wavefunctions of Bloch Electrons in Rational and Irrational Magnetic Fields, Phys. Rev. B, 14 (1976) 2239.
    • (1976) Phys. Rev. B. , vol.14 , pp. 2239
    • Hofstadter, D.R.1
  • 103
    • 35748971582 scopus 로고
    • States and representations in statistical mechanics
    • edited by Streater R. F. Academic Press, New York
    • HUGENHOLTZ N. M., States and Representations in Statistical Mechanics, in Mathematics of Contemporary Physics, edited by Streater R. F. (Academic Press, New York) 1972.
    • (1972) Mathematics of Contemporary Physics
    • Hugenholtz, N.M.1
  • 104
    • 0004270943 scopus 로고
    • 3rd edition Springer, Berlin and New York
    • HUSEMOLLER D., Fibre Bundles, 3rd edition (Springer, Berlin and New York) 1994.
    • (1994) Fibre Bundles
    • Husemoller, D.1
  • 106
    • 0039768795 scopus 로고    scopus 로고
    • Reduction of Jacobi manifolds
    • IBORT L. A., DELEON M. and MARMO G., Reduction of Jacobi Manifolds, J. Phys. A, 30 (1997) 2783.
    • (1997) J. Phys. A , vol.30 , pp. 2783
    • Ibort, L.A.1    Deleon, M.2    Marmo, G.3
  • 107
    • 0034165370 scopus 로고    scopus 로고
    • Bi-hamiltonian structures and stäckel separability
    • IBORT L. A., MAGRI F. and MARMO G., Bi-Hamiltonian Structures and Stäckel Separability, J. Geom. Phys., 33 (2000) 210.
    • (2000) J. Geom. Phys. , vol.33 , pp. 210
    • Ibort, L.A.1    Magri, F.2    Marmo, G.3
  • 108
    • 34250926633 scopus 로고
    • Uber die multiplikation quantenmechanischer grossen
    • JORDAN P., Uber die Multiplikation Quantenmechanischer Grossen, Z. Phys., 87 (1934) 505.
    • (1934) Z. Phys. , vol.87 , pp. 505
    • Jordan, P.1
  • 109
    • 0002266897 scopus 로고
    • On an algebraic generalization of the quantum mechanical formalism
    • JORDAN P., VON NEUMANN J. and WIGNER E. P., On an Algebraic Generalization of the Quantum Mechanical Formalism, Ann. Math., 35 (1934) 29.
    • (1934) Ann. Math. , vol.35 , pp. 29
    • Jordan, P.1    Von Neumann, J.2    Wigner, E.P.3
  • 114
    • 0033419403 scopus 로고    scopus 로고
    • Merits and demerits of the orbit method
    • KIRILLOV A. A., Merits and Demerits of the Orbit Method, Bull. Am. Math. Soc., 36 (1999) 433.
    • (1999) Bull. Am. Math. Soc. , vol.36 , pp. 433
    • Kirillov, A.A.1
  • 115
    • 0002535842 scopus 로고
    • Quantization and unitary representations part I. Prequantization
    • Springer-Verlag, Berlin
    • KONSTANT B., Quantization and Unitary Representations Part I. Prequantization, in Lect. Notes Math. 170 (Springer-Verlag, Berlin) 1970.
    • (1970) Lect. Notes Math. , vol.170
    • Konstant, B.1
  • 116
    • 33746765643 scopus 로고    scopus 로고
    • Closed formula for the metric in the hilbert space of a pt-symmetric model
    • KREJCIRIK D., BILA H. and ZNOJIL M., Closed Formula for the Metric in the Hilbert Space of a PT-Symmetric Model, J. Phys. A, 39 (2006) 10143.
    • (2006) J. Phys. A , vol.39 , pp. 10143
    • Krejcirik, D.1    Bila, H.2    Znojil, M.3
  • 117
    • 12344271673 scopus 로고
    • Statistical mechanical theory of irreversible processes. I. general theory and simple applications to magnetic and conduction problems
    • KUBO R., Statistical Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems, J. Phys. Soc. Jpn., 12 (1957) 570.
    • (1957) J. Phys. Soc. Jpn. , vol.12 , pp. 570
    • Kubo, R.1
  • 118
    • 0041751162 scopus 로고
    • Memoire sur la theorie de la variation des elements des planetes
    • LAGRANGE J. L., Memoire sur la Theorie de la Variation des Elements des Planetes, Mem. Cl. Sci. Math. Phys. Ins. France (1808) 1-72.
    • (1808) Mem. Cl. Sci. Math. Phys. Ins. France , pp. 1-72
    • Lagrange, J.L.1
  • 120
    • 36449003784 scopus 로고
    • Recursion operators meaning and existence for completely integrable systems
    • LANDI G., MARMO G. and VILASI G., Recursion Operators Meaning and Existence for Completely Integrable Systems, J. Math. Phys., 35 (1994) 808.
    • (1994) J. Math. Phys. , vol.35 , pp. 808
    • Landi, G.1    Marmo, G.2    Vilasi, G.3
  • 122
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations and solitary waves
    • LAX P. D., Integrals of Nonlinear Equations and Solitary Waves, Commun. Pure Appl. Math., XXI (1968) 467.
    • (1968) Commun. Pure Appl. Math. , vol.21 , pp. 467
    • Lax, P.D.1
  • 123
    • 84980148156 scopus 로고
    • Periodic solutions of the KdV equation
    • LAX P. D., Periodic Solutions of the KdV Equation, Commun. Pure Appl. Math., XXVIII (1975) 141.
    • (1975) Commun. Pure Appl. Math. , vol.28 , pp. 141
    • Lax, P.D.1
  • 124
    • 0000991407 scopus 로고
    • Almost periodic solutions of the KdV equation
    • LAX P. D., Almost Periodic Solutions of the KdV Equation, Siam Rev., 18 (1976) 351.
    • (1976) Siam Rev. , vol.18 , pp. 351
    • Lax, P.D.1
  • 126
    • 0011171790 scopus 로고    scopus 로고
    • Scalar charged particle in wigner-moyal phase space. Constant magnetic field
    • LEV B. I., SEMENOV A. A. and USENKO C. V., Scalar Charged Particle in Wigner-Moyal Phase Space. Constant Magnetic Field, J. Russian Laser Res., 23 (2002) 347.
    • (2002) J. Russian Laser Res. , vol.23 , pp. 347
    • Lev, B.I.1    Semenov, A.A.2    Usenko, C.V.3
  • 128
    • 44949275942 scopus 로고
    • On the extended feynman formula for the harmonic oscillator
    • LIANG J. Q. and MORANDI G., On the Extended Feynman Formula for the Harmonic Oscillator, Phys. Lett. A, 160 (1991) 9.
    • (1991) Phys. Lett. A , vol.160 , pp. 9
    • Liang, J.Q.1    Morandi, G.2
  • 129
    • 0000633925 scopus 로고
    • Les variétés de Jacobi et leurs algébres de lie associées
    • LICHNEROWICZ A., Les Variétés de Jacobi et Leurs Algébres de Lie Associées, J. Math. Pure Appl., 57 (1978) 453.
    • (1978) J. Math. Pure Appl. , vol.57 , pp. 453
    • Lichnerowicz, A.1
  • 130
    • 0039835161 scopus 로고    scopus 로고
    • Dynamical symmetries, non-cartan symmetries and superintegrability of the n-Dimensional harmonic oscillator
    • LOPEZ C., MARTINEZ E. and RAÑADA M. F., Dynamical Symmetries, Non-Cartan Symmetries and Superintegrability of the n-Dimensional Harmonic Oscillator, J. Phys. A: Math. Gen., 32 (1999) 1241.
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 1241
    • Lopez, C.1    Martinez, E.2    Rañada, M.F.3
  • 131
    • 0031210552 scopus 로고    scopus 로고
    • Wigner's problem for a precessing magnetic dipole
    • LOPEZ-PEÑA R., MAN'KO V. I. and MARMO G., Wigner's Problem for a Precessing Magnetic Dipole, Phys. Rev. A, 56 (1997) 1126.
    • (1997) Phys. Rev. A , vol.56 , pp. 1126
    • Lopez-Peña, R.1    Man'Ko, V.I.2    Marmo, G.3
  • 134
    • 36749117832 scopus 로고
    • A simple model of the integrable hamiltonian equation
    • MAGRI F., A Simple Model of the Integrable Hamiltonian Equation, J. Math. Phys., 19 (1978) 1156.
    • (1978) J. Math. Phys. , vol.19 , pp. 1156
    • Magri, F.1
  • 136
    • 0012363782 scopus 로고    scopus 로고
    • Alternative commutation relations, star products and tomography
    • MAN'KO O. V., MAN'KO V. I. and MARMO G., Alternative Commutation Relations, Star Products and Tomography, J. Phys. A, 35 (2002) 699.
    • (2002) J. Phys. A , vol.35 , pp. 699
    • Man'Ko, O.V.1    Man'Ko, V.I.2    Marmo, G.3
  • 137
    • 0037838283 scopus 로고    scopus 로고
    • Star-product of generalized wigner-weyl symbols on SU (2) group, deformations and tomographic probability distribution
    • MAN'KO O. V., MAN'KO V. I. and MARMO G., Star-Product of Generalized Wigner-Weyl Symbols on SU (2) Group, Deformations and Tomographic Probability Distribution, Phys. Scr., 62 (2000) 446.
    • (2000) Phys. Scr. , vol.62 , pp. 446
    • Man'Ko, O.V.1    Man'Ko, V.I.2    Marmo, G.3
  • 138
    • 0037492205 scopus 로고    scopus 로고
    • Probability distributions and hilbert spaces quantum and classical systems
    • MAN'KO V. I. and MARMO G., Probability Distributions and Hilbert Spaces Quantum and Classical Systems, Phys. Scr., 60 (1999) 111.
    • (1999) Phys. Scr. , vol.60 , pp. 111
    • Man'Ko, V.I.1    Marmo, G.2
  • 139
    • 0039131146 scopus 로고    scopus 로고
    • Aspects of nonlinear and noncanonical transformations in quantum mechanics
    • MAN'KO V. I. and MARMO G., Aspects of Nonlinear and Noncanonical Transformations in Quantum Mechanics, Phys. Scr., 58 (1998) 224.
    • (1998) Phys. Scr. , vol.58 , pp. 224
    • Man'Ko, V.I.1    Marmo, G.2
  • 141
    • 0000272098 scopus 로고
    • Physical nonlinear aspects of classical and quantum q-oscillators
    • MAN'KO V. I., MARMO G., SOLIMENO S. and ZACCARIA F., Physical Nonlinear Aspects of Classical and Quantum Q-Oscillators, Int. J. Mod. Phys. A, 8 (1993) 3577.
    • (1993) Int. J. Mod. Phys. A , vol.8 , pp. 3577
    • Man'Ko, V.I.1    Marmo, G.2    Solimeno, S.3    Zaccaria, F.4
  • 143
    • 52349109499 scopus 로고    scopus 로고
    • The geometry of density states, positive maps and tomograms
    • edited by Gruber B., Marmo G. and Yoshinaga N. Kluwer, New York
    • MAN'KO V. I., MARMO G., SUDARSHAN E. C. G. and ZACCARIA F., The Geometry of Density States, Positive Maps and Tomograms, in Symmetries in Science XI, edited by Gruber B., Marmo G. and Yoshinaga N. (Kluwer, New York) 2004.
    • (2004) Symmetries in Science XI
    • Man'Ko, V.I.1    Marmo, G.2    Sudarshan, E.C.G.3    Zaccaria, F.4
  • 145
    • 0034648202 scopus 로고    scopus 로고
    • Inner composition law for pure states as a purificatin of impure states
    • MAN'KO V. I., MARMO G., SUDARSHAN E. C. G. and ZACCARIA F., Inner Composition Law for Pure States as a Purificatin of Impure States, Phys. Lett. A, 273 (2000) 31.
    • (2000) Phys. Lett. A , vol.273 , pp. 31
    • Man'Ko, V.I.1    Marmo, G.2    Sudarshan, E.C.G.3    Zaccaria, F.4
  • 147
    • 1542532457 scopus 로고    scopus 로고
    • Entanglement in probability representation of quantum states and tomographic criterion of separability
    • MAN'KO V. I., MARMO G., SUDARSHAN E. C. G. and ZACCARIA F., Entanglement in Probability Representation of Quantum States and Tomographic Criterion of Separability, J. Opt. B: Quantum Semiclass. Opt., 6 (2004) 172.
    • (2004) J. Opt. B: Quantum. Semiclass. Opt. , vol.6 , pp. 172
    • Man'Ko, V.I.1    Marmo, G.2    Sudarshan, E.C.G.3    Zaccaria, F.4
  • 149
    • 0001480918 scopus 로고
    • A generalization of the Jordan-Wigner map classical versions and its Q-deformations
    • MAN'KO V. I., MARMO G., VITALE P. and ZACCARIA F., A Generalization of the Jordan-Wigner Map Classical Versions and its q-Deformations, Int. J. Mod. Phys. A, 9 (1994) 5541.
    • (1994) Int. J. Mod. Phys. A , vol.9 , pp. 5541
    • Man'Ko, V.I.1    Marmo, G.2    Vitale, P.3    Zaccaria, F.4
  • 150
    • 0000290608 scopus 로고    scopus 로고
    • Wigner's problem and alternative commutation relations for quantum mechanics
    • MAN'KO V. I., MARMO G., ZACCARIA F. and SUDARSHAN E. C. G., Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics, Int. J. Mod. Phys. B, 11 (1996) 1281.
    • (1996) Int. J. Mod. Phys. B. , vol.11 , pp. 1281
    • Man'Ko, V.I.1    Marmo, G.2    Zaccaria, F.3    Sudarshan, E.C.G.4
  • 151
    • 78651499117 scopus 로고
    • Equivalent lagrangians and quasi-canonical transformations
    • edited by James A., Janssen T. and Boon M. Springer-Verlag
    • MARMO G., Equivalent Lagrangians and Quasi-Canonical Transformations, in Group Theoretical Methods in Physics, edited by James A., Janssen T. and Boon M. (Springer-Verlag) 1976.
    • (1976) Group Theoretical Methods in Physics
    • Marmo, G.1
  • 152
    • 84914937209 scopus 로고
    • Nijenhuis operators in classical dynamics
    • USSR Academy of Sciences, Yurmala, Latvian SSR
    • MARMO G., Nijenhuis Operators in Classical Dynamics, in Seminar on Group Theoretical Methods in Physics (USSR Academy of Sciences, Yurmala, Latvian SSR) 1985.
    • (1985) Seminar on Group Theoretical Methods in Physics
    • Marmo, G.1
  • 153
    • 78651480674 scopus 로고    scopus 로고
    • The quantum-classical transition for systems with alternative hamiltonian descriptions
    • Real Sociedad Matematica Española, Madrid
    • MARMO G., The Quantum-Classical Transition for Systems with Alternative Hamiltonian Descriptions, in Proceedings of the IX Fall Workshop on Geometry and Physics (Real Sociedad Matematica Española, Madrid) 2001.
    • (2001) Proceedings of the IX Fall Workshop on Geometry and Physics
    • Marmo, G.1
  • 154
    • 0036119742 scopus 로고    scopus 로고
    • Alternative commutation relations and quantum Bi-hamiltonian systems
    • MARMO G., Alternative Commutation Relations and Quantum Bi-Hamiltonian Systems, Acta Appl. Math., 70 (2002) 161.
    • (2002) Acta Appl. Math. , vol.70 , pp. 161
    • Marmo, G.1
  • 155
    • 34547574658 scopus 로고    scopus 로고
    • The inverse problem for quantum systems
    • edited by Sarlet W. and Cantrijn F. Gent Academia Press, Gent 2003
    • MARMO G., The Inverse Problem for Quantum Systems, in Applied Differential Geometry and Mechanics, edited by Sarlet W. and Cantrijn F. (Gent Academia Press, Gent) 2003.
    • Applied Differential Geometry and Mechanics
    • Marmo, G.1
  • 156
    • 45249127198 scopus 로고
    • The inverse problem with symmetries and the appearance of cohomologies in classical lagrangian dynamics
    • MARMO G. and MORANDI G., The Inverse Problem with Symmetries and the Appearance of Cohomologies in Classical Lagrangian Dynamics, Rep. Math. Phys., 28 (1989) 389.
    • (1989) Rep. Math. Phys. , vol.28 , pp. 389
    • Marmo, G.1    Morandi, G.2
  • 158
    • 51249174371 scopus 로고
    • A geometrical approach to the Hamilton-Jacobi form of dynamics and its generalizations
    • MARMO G., MORANDI G. and MUKUNDA N., A Geometrical Approach to the Hamilton-Jacobi Form of Dynamics and its Generalizations, Riv. Nuovo Cimento, 13, N. 8 (1990) 1.
    • (1990) Riv. Nuovo Cimento , vol.13 , Issue.8 , pp. 1
    • Marmo, G.1    Morandi, G.2    Mukunda, N.3
  • 159
    • 0002873842 scopus 로고
    • Symmetries in the lagrangian and hamiltonian formalism. The equivariant inverse problem
    • edited by Gruber B. and Iachello E. Plenum Press, New York
    • MARMO G., MORANDI G. and RUBANO C., Symmetries in the Lagrangian and Hamiltonian Formalism. The Equivariant Inverse Problem, in Symmetries in Science III, edited by Gruber B. and Iachello E. (Plenum Press, New York) 1983.
    • (1983) Symmetries in Science III
    • Marmo, G.1    Morandi, G.2    Rubano, C.3
  • 160
    • 0037064102 scopus 로고    scopus 로고
    • Alternative structures and Bi-hamiltonian systems
    • MARMO G., MORANDI G., SIMONI A. and VENTRIGLIA F., Alternative Structures and Bi-Hamiltonian Systems, J. Phys. A, 35 (2002) 8393.
    • (2002) J. Phys. A , vol.35 , pp. 8393
    • Marmo, G.1    Morandi, G.2    Simoni, A.3    Ventriglia, F.4
  • 162
    • 0002378221 scopus 로고
    • Relativistic particle dynamics-lagrangian proof of the no-interaction theorem
    • MARMO G., MUKUNDA N. and SUDARSHAN E. C. G., Relativistic Particle Dynamics-Lagrangian Proof of the No-Interaction Theorem, Phys. Rev. D, 30 (1984) 2110.
    • (1984) Phys. Rev. D , vol.30 , pp. 2110
    • Marmo, G.1    Mukunda, N.2    Sudarshan, E.C.G.3
  • 163
    • 45949122578 scopus 로고
    • Alternative lagrangians for a charged particle in a magnetic field
    • MARMO G. and RUBANO C., Alternative Lagrangians for a Charged Particle in a Magnetic Field, Phys. Lett. A, 119 (1987) 321.
    • (1987) Phys. Lett. A , vol.119 , pp. 321
    • Marmo, G.1    Rubano, C.2
  • 164
    • 51249182643 scopus 로고
    • Ambiguities in the lagrangian and hamiltonian formalisms transformation properties
    • MARMO G. and SALETAN E. J., Ambiguities in the Lagrangian and Hamiltonian Formalisms Transformation Properties, Nuovo Cimento B, 40 (1977) 67.
    • (1977) Nuovo Cimento B. , vol.40 , pp. 67
    • Marmo, G.1    Saletan, E.J.2
  • 165
    • 78651505562 scopus 로고
    • Q-equivalent particle hamiltonians. III. The two-dimensional quantum oscillator
    • MARMO G. and SALETAN E. J., q-Equivalent Particle Hamiltonians. III. The Two-Dimensional Quantum Oscillator, Hadronic J., 3 (1980) 1644.
    • (1980) Hadronic J. , vol.3 , pp. 1644
    • Marmo, G.1    Saletan, E.J.2
  • 166
    • 0041867680 scopus 로고
    • Bi-hamiltonian dynamical systems and the quadratic-hamiltonian theorem
    • MARMO G., SALETAN E. J., SCHMID R. and SIMONI A., Bi-Hamiltonian Dynamical Systems and the Quadratic-Hamiltonian Theorem, Nuovo Cimento B, 100 (1987) 297.
    • (1987) Nuovo Cimento B. , vol.100 , pp. 297
    • Marmo, G.1    Saletan, E.J.2    Schmid, R.3    Simoni, A.4
  • 168
    • 78651484828 scopus 로고    scopus 로고
    • Alternative hamiltonian descriptions for quantum systems
    • edited by Alvarez-Estrada R. F., Dobado A., Fernandez L. A., Martin-Delgado M. A. and Munoz Sudupe A. Aula Documental de Investigacion, Madrid
    • MARMO G., SCOLARICI G., SIMONI A. and VENTRIGLIA F., Alternative Hamiltonian Descriptions for Quantum Systems, in Encuentro de Fisica Fundamental, edited by Alvarez-Estrada R. F., Dobado A., Fernandez L. A., Martin-Delgado M. A. and Munoz Sudupe A. (Aula Documental de Investigacion, Madrid) 2005.
    • (2005) Encuentro de Fisica Fundamental
    • Marmo, G.1    Scolarici, G.2    Simoni, A.3    Ventriglia, F.4
  • 169
    • 23944485526 scopus 로고    scopus 로고
    • Quantum Bi-hamiltonian systems, alternative structures and Bi-unitary transformations
    • MARMO G., SCOLARICI G., SIMONI A. and VENTRIGLIA F., Quantum Bi-Hamiltonian Systems, Alternative Structures and Bi-Unitary Transformations, Note Matematica, 23 (2004) 173.
    • (2004) Note Matematica , vol.23 , pp. 173
    • Marmo, G.1    Scolarici, G.2    Simoni, A.3    Ventriglia, F.4
  • 171
    • 23944493186 scopus 로고    scopus 로고
    • Alternative structures and Bi-hamiltonian systems on a hilbert space
    • MARMO G., SCOLARICI G., SIMONI A. and VENTRIGLIA F., Alternative Structures and Bi-Hamiltonian Systems on a Hilbert Space, J. Phys. A, 38 (2005) 3813.
    • (2005) J. Phys. A , vol.38 , pp. 3813
    • Marmo, G.1    Scolarici, G.2    Simoni, A.3    Ventriglia, F.4
  • 173
    • 23944506868 scopus 로고    scopus 로고
    • Classical and quantum systems alternative hamiltonian descriptions
    • MARMO G., SCOLARICI G., SIMONI A. and VENTRIGLIA F., Classical and Quantum Systems Alternative Hamiltonian Descriptions, Theor. Math. Phys., 144 (2005) 1190.
    • (2005) Theor. Math. Phys. , vol.144 , pp. 1190
    • Marmo, G.1    Scolarici, G.2    Simoni, A.3    Ventriglia, F.4
  • 174
    • 0001233427 scopus 로고    scopus 로고
    • Bi-hamiltonian quantum systems and weyl quantization
    • MARMO G., SIMONI A. and VENTRIGLIA F., Bi-Hamiltonian Quantum Systems and Weyl Quantization, Rep. Math. Phys., 48 (2001) 149.
    • (2001) Rep. Math. Phys. , vol.48 , pp. 149
    • Marmo, G.1    Simoni, A.2    Ventriglia, F.3
  • 175
    • 0038349511 scopus 로고    scopus 로고
    • Quantum systems real spectra and non-hermitian (Hamiltonian)
    • MARMO G., SIMONI A. and VENTRIGLIA F., Quantum Systems Real Spectra and Non-Hermitian (Hamiltonian) Operators, Rep. Math. Phys., 51 (2003) 275.
    • (2003) Operators, Rep. Math. Phys. , vol.51 , pp. 275
    • Marmo, G.1    Simoni, A.2    Ventriglia, F.3
  • 177
    • 13844281800 scopus 로고    scopus 로고
    • Quantum systems and alternative unitary descriptions
    • MARMO G., SIMONI A. and VENTRIGLIA F., Quantum Systems and Alternative Unitary Descriptions, Int. J. Mod. Phys. A, 19 (2004) 2561.
    • (2004) Int. J. Mod. Phys. A , vol.19 , pp. 2561
    • Marmo, G.1    Simoni, A.2    Ventriglia, F.3
  • 178
    • 78651514760 scopus 로고    scopus 로고
    • Geometrical structures emerging from quantum mechanics
    • edited by Gallardo J. C. and Martinez E. Monografias de la Real Academia de Ciencias, Zaragoza
    • MARMO G., SIMONI A. and VENTRIGLIA F., Geometrical Structures Emerging from Quantum Mechanics, in Groups, Geometry and Physics, edited by Gallardo J. C. and Martinez E. (Monografias de la Real Academia de Ciencias, Zaragoza) 2006.
    • (2006) Groups, Geometry and Physics
    • Marmo, G.1    Simoni, A.2    Ventriglia, F.3
  • 179
    • 0000610551 scopus 로고
    • When do recursion operators generate new conservation laws?
    • MARMO G. and VILASI G., When do Recursion Operators Generate New Conservation Laws?, Phys. Lett. B, 277 (1992) 137.
    • (1992) Phys. Lett. B. , vol.277 , pp. 137
    • Marmo, G.1    Vilasi, G.2
  • 180
    • 0006347655 scopus 로고    scopus 로고
    • Symplectic structures and quantum mechanics
    • MARMO G. and VILASI G., Symplectic Structures and Quantum Mechanics, Mod. Phys. Lett. B, 10 (1996) 545.
    • (1996) Mod. Phys. Lett. B. , vol.10 , pp. 545
    • Marmo, G.1    Vilasi, G.2
  • 181
    • 0043141866 scopus 로고
    • Theory of many-particle systems. I
    • MARTIN P. C. and SCHWINGER J., Theory of Many-Particle Systems. I, Phys. Rev., 115 (1959) 1342.
    • (1959) Phys. Rev. , vol.115 , pp. 1342
    • Martin, P.C.1    Schwinger, J.2
  • 186
    • 0042770239 scopus 로고
    • The inverse problem in the calculus of variations and the geometry of the tangent bundle
    • MORANDI G., FERRARIO C., LOVECCHIO G., MARMO G. and RUBANO C., The Inverse Problem in the Calculus of Variations and the Geometry of the Tangent Bundle, Phys. Rep., 188 (1990) 147.
    • (1990) Phys. Rep. , vol.188 , pp. 147
    • Morandi, G.1    Ferrario, C.2    Lovecchio, G.3    Marmo, G.4    Rubano, C.5
  • 189
    • 78651479278 scopus 로고
    • Quantum mechanics as a statistical theory
    • MOYAL J. E., Quantum Mechanics as a Statistical Theory, Proc. Cambdridge Philos. Soc., 45 (1940) 90.
    • (1940) Proc. Cambdridge Philos. Soc. , vol.45 , pp. 90
    • Moyal, J.E.1
  • 190
    • 51249180278 scopus 로고
    • Algebraic aspects of the wigner distribution in quantum mechanics
    • MUKUNDA N., Algebraic Aspects of the Wigner Distribution in Quantum Mechanics, Pramana, 11 (1978) 1.
    • (1978) Pramana , vol.11 , pp. 1
    • Mukunda, N.1
  • 192
    • 0004092094 scopus 로고
    • Wolters-Noordhoff Publishing, Groningen
    • NAIMARK M. A., Normed Rings (Wolters-Noordhoff Publishing, Groningen) 1970.
    • (1970) Normed Rings
    • Naimark, M.A.1
  • 193
  • 194
    • 0001031484 scopus 로고
    • Jacobi-type identities for bilinear differential concomitants of certain tensor fields. I and II
    • 398
    • NIJENHUIS A., Jacobi-Type Identities for Bilinear Differential Concomitants of Certain Tensor Fields. I and II, Indag. Math., 17 (1955) 390; 398.
    • (1955) Indag. Math. , vol.17 , pp. 390
    • Nijenhuis, A.1
  • 195
    • 0001598231 scopus 로고
    • Complex analytic coordinates in almost complex manifolds
    • NIRENBERG L. and NEWLANDER A., Complex Analytic Coordinates in Almost Complex Manifolds, Ann. Math., 65 (1957) 391.
    • (1957) Ann. Math. , vol.65 , pp. 391
    • Nirenberg, L.1    Newlander, A.2
  • 196
    • 21144474916 scopus 로고
    • Self-adjointness of operators in Wigner's commutation relations
    • OHNUKI Y. and WATANABE S., Self-Adjointness of Operators in Wigner's Commutation Relations, J. Math. Phys., 33 (1992) 3653.
    • (1992) J. Math. Phys. , vol.33 , pp. 3653
    • Ohnuki, Y.1    Watanabe, S.2
  • 197
    • 78651475390 scopus 로고
    • Generalized theory of interference and its applications
    • Oxford University Press, Oxford
    • PANCHARATNAM S., Generalized Theory of Interference and its Applications, in Collected Works of S. Pancharatnam (Oxford University Press, Oxford) 1975.
    • (1975) Collected Works of S. Pancharatnam
    • Pancharatnam, S.1
  • 198
    • 0002379655 scopus 로고
    • Mathematical aspects of the weyl correspondence
    • POOL J. C. T., Mathematical Aspects of the Weyl Correspondence, J. Math. Phys., 7 (1966) 66.
    • (1966) J. Math. Phys. , vol.7 , pp. 66
    • Pool, J.C.T.1
  • 199
    • 36149004685 scopus 로고
    • The quantum-mechanical equations of motion and commutation relations
    • PUTNAM C. R., The Quantum-Mechanical Equations of Motion and Commutation Relations, Phys. Rev., 83 (1951) 1047.
    • (1951) Phys. Rev. , vol.83 , pp. 1047
    • Putnam, C.R.1
  • 200
    • 0034347179 scopus 로고    scopus 로고
    • Dynamical symmetries, bi-hamiltonian structures and superintegrability of n = 2 systems
    • RAÑADA M. F., Dynamical Symmetries, Bi-Hamiltonian Structures and Superintegrability of n = 2 Systems, J. Math. Phys., 41 (2000) 2121.
    • (2000) J. Math. Phys. , vol.41 , pp. 2121
    • Rañada, M.F.1
  • 206
    • 0007393035 scopus 로고
    • Algèbres associatives locales sur l'espace des sections d'un fibré àdroites
    • RUBIO R., Algèbres Associatives Locales sur l'Espace des Sections d'un Fibré àDroites, C. R. Acad. Sci. Paris, Sér. I, n. 14, 699 (1984) 821.
    • (1984) C. R. Acad. Sci. Paris, Sér. I , vol.699 , Issue.14 , pp. 821
    • Rubio, R.1
  • 207
    • 0031144782 scopus 로고    scopus 로고
    • The geometric phase and ray space isometries
    • SAMUEL J., The Geometric Phase and Ray Space Isometries, Pramana J. Phys., 48 (1997) 959.
    • (1997) Pramana J. Phys. , vol.48 , pp. 959
    • Samuel, J.1
  • 209
    • 0002996452 scopus 로고
    • On the differential operators of first order in tensor calculus
    • Cremonese, Roma
    • SCHOUTEN J. A., On the Differential Operators of First Order in Tensor Calculus, in Conv. Int. Geom. Diff. Italia (Cremonese, Roma) 1954.
    • (1954) Conv. Int. Geom. Diff. Italia
    • Schouten, J.A.1
  • 211
    • 36149008027 scopus 로고
    • A note on commutators in quantized field theories
    • SCHWEBER S. S., A Note on Commutators in Quantized Field Theories, Phys. Rev., 78 (1950) 613.
    • (1950) Phys. Rev. , vol.78 , pp. 613
    • Schweber, S.S.1
  • 212
    • 0008081622 scopus 로고
    • On feynman quantization
    • SCHWEBER S. S., On Feynman Quantization, J. Math. Phys., 3 (1962) 831.
    • (1962) J. Math. Phys. , vol.3 , pp. 831
    • Schweber, S.S.1
  • 217
    • 0001402930 scopus 로고
    • Quantum theory in real hilbert space
    • STUECKELBERG E. C. G., Quantum Theory in Real Hilbert Space, Helv. Phys. Acta, 33 (1960) 727; 34 (1961) 621.
    • (1960) Helv. Phys. Acta , vol.33 , pp. 727
    • Stueckelberg, E.C.G.1
  • 218
    • 78651470305 scopus 로고    scopus 로고
    • 34 1961 621
    • 34 (1961) 621.
  • 220
    • 0001130734 scopus 로고
    • Variations on a theme by schwinger and weyl
    • VARADARAJAN V. S., Variations on a Theme by Schwinger and Weyl, Lett. Math. Phys., 34 (1995) 319.
    • (1995) Lett. Math. Phys. , vol.34 , pp. 319
    • Varadarajan, V.S.1
  • 221
    • 0037055824 scopus 로고    scopus 로고
    • Alternative hamiltonian descriptions for quantum systems and non-hermitian operators with real spectra
    • VENTRIGLIA F., Alternative Hamiltonian Descriptions for Quantum Systems and non-Hermitian Operators with Real Spectra, Mod. Phys. Lett. A, 17 (2002) 1589.
    • (2002) Mod. Phys. Lett. A , vol.17 , pp. 1589
    • Ventriglia, F.1
  • 223
    • 0000557239 scopus 로고
    • Warscheinlichtkeitstheoretische aufbau der quantenmechanik
    • VON NEUMANN J., Warscheinlichtkeitstheoretische Aufbau der Quantenmechanik, Goett. Nachr., 10 (1927) 245
    • (1927) Goett. Nachr. , vol.10 , pp. 245
    • Von Neumann, J.1
  • 224
    • 78651477603 scopus 로고
    • edited by Taub A. H., Pergamon Press, Oxford
    • in J. von Neumann Collected Papers, edited by Taub A. H., Vol. I (Pergamon Press, Oxford) 1961.
    • (1961) J. Von Neumann Collected Papers , vol.1
  • 226
    • 0003429685 scopus 로고
    • English translation:, Princeton University Press, Princeton
    • (English translation: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton) 1955).
    • (1955) Mathematical Foundations of Quantum. Mechanics
  • 229
    • 4243251041 scopus 로고
    • Bethe-ansatz for the bloch electrons in a magnetic field
    • WIEGMANN P. B. and ZABRODIN A. V., Bethe-Ansatz for the Bloch Electrons in a Magnetic Field, Phys. Rev. Lett., 72 (1994) 1890.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1890
    • Wiegmann, P.B.1    Zabrodin, A.V.2
  • 230
    • 0000088221 scopus 로고
    • Uber die operation der zeitumkehr in der quantenmechanik
    • WIGNER E. P., Uber die Operation der Zeitumkehr in der Quantenmechanik, Gott. Nachr., 31 (1932) 546.
    • (1932) Gott. Nachr. , vol.31 , pp. 546
    • Wigner, E.P.1
  • 231
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • WIGNER E. P., On the Quantum Correction for Thermodynamic Equilibrium, Phys. Rev., 40 (1932) 749.
    • (1932) Phys. Rev. , vol.40 , pp. 749
    • Wigner, E.P.1
  • 232
    • 36149011058 scopus 로고
    • Do the equations of motion determine the quantum mechanical commutation relations?
    • WIGNER E. P., Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?, Phys Rev., 77 (1950) 711.
    • (1950) Phys. Rev. , vol.77 , pp. 711
    • Wigner, E.P.1
  • 234
    • 33745445626 scopus 로고
    • The definition of the lie derivative
    • WILLMORE T. J., The Definition of the Lie Derivative, Proc. Edinburgh. Math. Soc., 12 (1960) 27.
    • (1960) Proc. Edinburgh. Math. Soc. , vol.12 , pp. 27
    • Willmore, T.J.1
  • 235
    • 0012900542 scopus 로고
    • The unboundedness of quantum-mechanical matrices
    • WINTNER A., The Unboundedness of Quantum-Mechanical Matrices, Phys. Rev., 71 (1947) 738.
    • (1947) Phys. Rev. , vol.71 , pp. 738
    • Wintner, A.1
  • 236
    • 0001538342 scopus 로고
    • Quantum mechanics without probability amplitudes
    • WOOTTERS W. K., Quantum Mechanics Without Probability Amplitudes, Found. Phys., 16 (1986) 391.
    • (1986) Found. Phys. , vol.16 , pp. 391
    • Wootters, W.K.1
  • 237
    • 33744505701 scopus 로고
    • A wigner-function formulation of finite-state quantum mechanics
    • WOOTTERS W. K., A Wigner-Function Formulation of Finite-State Quantum Mechanics, Ann. Phys. (New York), 176 (1987) 1.
    • (1987) Ann. Phys. (New York) , vol.176 , pp. 1
    • Wootters, W.K.1
  • 238
    • 36149008336 scopus 로고
    • A note on the quantum rule of the harmonic oscillator
    • YANG L. M., A Note on the Quantum Rule of the Harmonic Oscillator, Phys. Rev., 84 (1951) 788.
    • (1951) Phys. Rev. , vol.84 , pp. 788
    • Yang, L.M.1
  • 239
    • 36149008019 scopus 로고
    • Magnetic translation groups
    • ZAK J., Magnetic Translation Groups, Phys. Rev. A, 134 (1964) 1602.
    • (1964) Phys. Rev. A , vol.134 , pp. 1602
    • Zak, J.1
  • 240
    • 36049057875 scopus 로고
    • Dynamics of electrons in external fields
    • ZAK J., Dynamics of Electrons in External Fields, Phys. Rev., 168 (1968) 686.
    • (1968) Phys. Rev. , vol.168 , pp. 686
    • Zak, J.1
  • 241
    • 0012283099 scopus 로고
    • Weyl-heisenberg group and magnetic translations in a finite phase space
    • ZAK J., Weyl-Heisenberg Group and Magnetic Translations in a Finite Phase Space, Phys. Rev. B, 39 (1989) 694.
    • (1989) Phys. Rev. B. , vol.39 , pp. 694
    • Zak, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.