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Volumn 128, Issue 3, 2004, Pages 197-251

Feynman path integrals as analysis on path space by time slicing approximation

Author keywords

Fourier integral operator; Path integrals; Stochastic analysis

Indexed keywords


EID: 1542613359     PISSN: 00074497     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulsci.2004.01.002     Document Type: Article
Times cited : (31)

References (22)
  • 2
    • 85171876123 scopus 로고
    • A family of integrals serving to connect the Wiener and Feynman integrals
    • Cameron R.H. A family of integrals serving to connect the Wiener and Feynman integrals J. Math. Phys. 39 1960 126-140
    • (1960) J. Math. Phys. , vol.39 , pp. 126-140
    • Cameron, R.H.1
  • 3
    • 34547361024 scopus 로고
    • Space-time approach to non-relativistic quantum mechanics
    • Feynman R.P. Space-time approach to non-relativistic quantum mechanics Rev. Modern Phys. 20 1948 367-387
    • (1948) Rev. Modern Phys. , vol.20 , pp. 367-387
    • Feynman, R.P.1
  • 4
    • 84972584889 scopus 로고
    • Remarks on convergence of the Feynman path integrals
    • Fujiwara D. Remarks on convergence of the Feynman path integrals Duke Math. J. 47 1980 559-600
    • (1980) Duke Math. J. , vol.47 , pp. 559-600
    • Fujiwara, D.1
  • 5
    • 84972537278 scopus 로고
    • The stationary phase method with an estimate of the remainder term on a space of large dimension
    • Fujiwara D. The stationary phase method with an estimate of the remainder term on a space of large dimension Nagoya Math. J. 124 1991 61-97
    • (1991) Nagoya Math. J. , vol.124 , pp. 61-97
    • Fujiwara, D.1
  • 6
    • 0039319395 scopus 로고
    • Some Feynman path integrals as oscillatory integrals over a Sobolev manifold
    • Preprint
    • D. Fujiwara, Some Feynman path integrals as oscillatory integrals over a Sobolev manifold, Preprint, 1992
    • (1992)
    • Fujiwara, D.1
  • 7
    • 0010886936 scopus 로고
    • Some Feynman path integrals as oscillatory integrals over a Sobolev manifold
    • Springer
    • Fujiwara D. Some Feynman path integrals as oscillatory integrals over a Sobolev manifold Lecture Notes in Math. vol. 1540 1993 39-53 Springer
    • (1993) Lecture Notes in Math. , vol.1540 , pp. 39-53
    • Fujiwara, D.1
  • 9
    • 0039319396 scopus 로고    scopus 로고
    • A proof of estimates of Kumanogo-Taniguchi type for multi-product of Fourier integral operators
    • Fujiwara D. Kumano-go N. Taniguchi K. A proof of estimates of Kumanogo-Taniguchi type for multi-product of Fourier integral operators Funkcial. Ekvac. 40 1997 459-470
    • (1997) Funkcial. Ekvac. , vol.40 , pp. 459-470
    • Fujiwara, D.1    Kumano-go, N.2    Taniguchi, K.3
  • 10
    • 0031116390 scopus 로고    scopus 로고
    • The time slicing approximation of the fundamental solution for the Schrödinger equation with electromagnetic fields
    • Fujiwara D. Tsuchida T. The time slicing approximation of the fundamental solution for the Schrödinger equation with electromagnetic fields J. Math. Soc. Japan 49 1997 299-327
    • (1997) J. Math. Soc. Japan , vol.49 , pp. 299-327
    • Fujiwara, D.1    Tsuchida, T.2
  • 11
    • 0031513612 scopus 로고    scopus 로고
    • On the formulation of Feynman path integral through broken line paths
    • Ichinose W. On the formulation of Feynman path integral through broken line paths Comm. Math. Phys. 189 1997
    • (1997) Comm. Math. Phys. , vol.189
    • Ichinose, W.1
  • 12
    • 0001455484 scopus 로고
    • Stochastic integral
    • Itô K. Stochastic integral Proc. Imp. Acad. Tokyo 20 1944 519-524
    • (1944) Proc. Imp. Acad. Tokyo , vol.20 , pp. 519-524
    • Itô, K.1
  • 13
    • 0000010533 scopus 로고
    • Generalized uniform complex measure in Hilbert space and its application to the Feynman path integrals
    • Berkeley: University of California Press
    • Itô K. Generalized uniform complex measure in Hilbert space and its application to the Feynman path integrals Proc. 5th Berkeley Sympos. Math. Statist. and Prob., vol. 2, part 1 1967 145-161 University of California Press Berkeley
    • (1967) Proc. 5th Berkeley Sympos. Math. Statist. and Prob. , vol.2 , Issue.PART 1 , pp. 145-161
    • Itô, K.1
  • 14
    • 84972579176 scopus 로고
    • A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
    • Kitada H. Kumano-go H. A family of Fourier integral operators and the fundamental solution for a Schrödinger equation Osaka J. Math. 18 1981 291-360
    • (1981) Osaka J. Math. , vol.18 , pp. 291-360
    • Kitada, H.1    Kumano-go, H.2
  • 16
    • 0041098797 scopus 로고
    • Fourier integral operators of multi-phase and the fundamental solution for a hyperbolic system
    • Kumano-go H. Taniguchi K. Fourier integral operators of multi-phase and the fundamental solution for a hyperbolic system Funkcial. Ekvac. 22 1979 161-196
    • (1979) Funkcial. Ekvac. , vol.22 , pp. 161-196
    • Kumano-go, H.1    Taniguchi, K.2
  • 17
    • 0039911796 scopus 로고
    • A construction of the fundamental solution for Schrödinger equations
    • Kumano-go N. A construction of the fundamental solution for Schrödinger equations J. Math. Sci. Univ. Tokyo 2 1995 441-498
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , pp. 441-498
    • Kumano-go, N.1
  • 18
    • 0039993567 scopus 로고    scopus 로고
    • A proof of H. Kumano-go-Taniguchi theorem for multi-products of Fourier integral operators
    • Kumano-go N. A proof of H. Kumano-go-Taniguchi theorem for multi-products of Fourier integral operators Osaka J. Math. 35 1998 357-380
    • (1998) Osaka J. Math. , vol.35 , pp. 357-380
    • Kumano-go, N.1
  • 20
    • 0000431067 scopus 로고
    • Feynman integrals and Schödinger equation
    • Nelson E. Feynman integrals and Schödinger equation J. Math. Phys. 5 1964 332-343
    • (1964) J. Math. Phys. , vol.5 , pp. 332-343
    • Nelson, E.1
  • 21
    • 0001736303 scopus 로고
    • A new representation for stochastic integrals and equations
    • Stratonovich R.L. A new representation for stochastic integrals and equations J. SIAM Control 4 2 1966 362-371
    • (1966) J. SIAM Control , vol.4 , Issue.2 , pp. 362-371
    • Stratonovich, R.L.1
  • 22
    • 51249171749 scopus 로고
    • Schrödinger evolution equations with magnetic fields
    • Yajima K. Schrödinger evolution equations with magnetic fields J. Analyse Math. 56 1991 29-76
    • (1991) J. Analyse Math. , vol.56 , pp. 29-76
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.