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Volumn 115, Issue 1-2, 2004, Pages 191-215

Some new developments in the theory of path integrals, with applications to quantum theory

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EID: 3543083421     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000019836.37663.d9     Document Type: Review
Times cited : (11)

References (77)
  • 1
    • 0346228350 scopus 로고    scopus 로고
    • Wiener and Feynman path integrals and their applications
    • S. Albeverio, Wiener and Feynman path integrals and their applications, in Proceedings of Symposia in Applied Mathematics, Vol. 52 (1997), pp. 163-194.
    • (1997) Proceedings of Symposia in Applied Mathematics , vol.52 , pp. 163-194
    • Albeverio, S.1
  • 3
    • 0039270665 scopus 로고    scopus 로고
    • The trace formula for Schrödinger operators from infinite dimensional oscillatory integrals
    • S. Albeverio, A. M. Boutet de Monvel-Berthier, and Z. Brzeźniak, The trace formula for Schrödinger operators from infinite dimensional oscillatory integrals, Math. Nachr. 182:21-65 (1996).
    • (1996) Math. Nachr. , vol.182 , pp. 21-65
    • Albeverio, S.1    Boutet De Monvel-Berthier, A.M.2    Brzeźniak, Z.3
  • 4
    • 43949175740 scopus 로고
    • Finite-dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
    • S. Albeverio and Z. Brzeźniak, Finite-dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions, J. Funct. Anal. 113:177-244 (1993).
    • (1993) J. Funct. Anal. , vol.113 , pp. 177-244
    • Albeverio, S.1    Brzeźniak, Z.2
  • 5
    • 21844523901 scopus 로고
    • Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields
    • S. Albeverio and Z. Brzeźniak, Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields, J. Math. Phys. 36:2135-2156 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 2135-2156
    • Albeverio, S.1    Brzeźniak, Z.2
  • 6
    • 0043227993 scopus 로고    scopus 로고
    • On the Schrödinger equation with potentials which are Laplace transforms of measures
    • S. Albeverio, Z. Brzeźniak, and Z. Haba, On the Schrödinger equation with potentials which are Laplace transforms of measures, Potential Anal. 9:65-82 (1998).
    • (1998) Potential Anal. , vol.9 , pp. 65-82
    • Albeverio, S.1    Brzeźniak, Z.2    Haba, Z.3
  • 8
    • 0035529587 scopus 로고    scopus 로고
    • Scattering theory for quantum fields with indefinite metric
    • S. Albeverio and H. Gottschalk, Scattering theory for quantum fields with indefinite metric, Comm. Math. Phys. 216:491-513 (2001).
    • (2001) Comm. Math. Phys. , vol.216 , pp. 491-513
    • Albeverio, S.1    Gottschalk, H.2
  • 9
    • 0036265666 scopus 로고    scopus 로고
    • Representing Euclidean quantum fields as scaling limit of particle systems
    • S. Albeverio, H. Gottschalk, and M. Yoshida, Representing Euclidean quantum fields as scaling limit of particle systems, J. Stat. Phys. 108:361-369 (2002).
    • (2002) J. Stat. Phys. , vol.108 , pp. 361-369
    • Albeverio, S.1    Gottschalk, H.2    Yoshida, M.3
  • 10
    • 0030209383 scopus 로고    scopus 로고
    • Convoluted generalized white noise, Schwinger functions, and their analytic continuation
    • S. Albeverio, H. Gottschalk, and J. L. Wu, Convoluted generalized white noise, Schwinger functions, and their analytic continuation, Rev. Math. Phys. 8:763-817 (1996).
    • (1996) Rev. Math. Phys. , vol.8 , pp. 763-817
    • Albeverio, S.1    Gottschalk, H.2    Wu, J.L.3
  • 11
    • 0031513489 scopus 로고    scopus 로고
    • Models of local relativistic quantum fields with indefinite metric (in all dimensions)
    • S. Albeverio, H. Gottschalk, and J. L. Wu, Models of local relativistic quantum fields with indefinite metric (in all dimensions), Comm. Math. Phys. 184:509-531 (1997).
    • (1997) Comm. Math. Phys. , vol.184 , pp. 509-531
    • Albeverio, S.1    Gottschalk, H.2    Wu, J.L.3
  • 13
    • 0038270666 scopus 로고    scopus 로고
    • Representation of the Belavkin equation via Feynman path integrals
    • S. Albeverio, G. Guatteri, and S. Mazzucchi, Representation of the Belavkin equation via Feynman path integrals, Probab. Theory Related Fields 125:365-380 (2003).
    • (2003) Probab. Theory Related Fields , vol.125 , pp. 365-380
    • Albeverio, S.1    Guatteri, G.2    Mazzucchi, S.3
  • 15
    • 85204046455 scopus 로고    scopus 로고
    • Rigorous Feynman path integrals, with applications to quantum theory, gauge fields, and topological invariants
    • SFB 611, Preprint, Bonn, to appear
    • S. Albeverio, A. Hahn, and A. Sengupta, Rigorous Feynman path integrals, with applications to quantum theory, gauge fields, and topological invariants, SFB 611, Preprint, Bonn, No. 58, 2003, to appear in Proc. Conf. Mathematical Legacy of Feynman's Path Integral, Lisbone 2003.
    • (2003) Proc. Conf. Mathematical Legacy of Feynman's Path Integral, Lisbone 2003 , vol.58
    • Albeverio, S.1    Hahn, A.2    Sengupta, A.3
  • 16
    • 0000352459 scopus 로고    scopus 로고
    • Représentation des solutions de l'équation de Belavkin pour la mesure quantique par une version rigoureuse de la formule d'intégration fonctionnelle de Menski
    • S. Albeverio, V. N. Kolokol'tsov, and O. G. Smolyanov, Représentation des solutions de l'équation de Belavkin pour la mesure quantique par une version rigoureuse de la formule d'intégration fonctionnelle de Menski, C. R. Acad. Sci. Paris Sér. I Math. 323:661-664 (1996).
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.323 , pp. 661-664
    • Albeverio, S.1    Kolokol'tsov, V.N.2    Smolyanov, O.G.3
  • 17
    • 0031260719 scopus 로고    scopus 로고
    • Continuous quantum measurement: Local and global approaches
    • S. Albeverio, V. N. Kolokol'tsov, and O. G. Smolyanov, Continuous quantum measurement: Local and global approaches, Rev. Math. Phys. 9:907-920 (1997).
    • (1997) Rev. Math. Phys. , vol.9 , pp. 907-920
    • Albeverio, S.1    Kolokol'tsov, V.N.2    Smolyanov, O.G.3
  • 22
    • 0000364933 scopus 로고
    • Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
    • S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms, Probab. Theory Related Fields 89:347-386 (1991).
    • (1991) Probab. Theory Related Fields , vol.89 , pp. 347-386
    • Albeverio, S.1    Röckner, M.2
  • 23
    • 0000079939 scopus 로고
    • Classical Dirichlet forms on topological vector spaces - The construction of the associated diffusion process
    • S. Albeverio and M. Röckner, Classical Dirichlet forms on topological vector spaces - The construction of the associated diffusion process, Probab. Theory Related Fields 83:405-434 (1989).
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 405-434
    • Albeverio, S.1    Röckner, M.2
  • 24
    • 0039561025 scopus 로고
    • Dirichlet forms, quantum fields, and stochastic quantization
    • Pitman Res. Notes Math. Ser., (Longman Sci. Tech., Harlow)
    • S. Albeverio and M. Röckner, Dirichlet forms, quantum fields, and stochastic quantization, in Stochastic Analysis, Path Integration, and Dynamics, Pitman Res. Notes Math. Ser., Vol. 200 (Longman Sci. Tech., Harlow, 1989), pp. 1-21.
    • (1989) Stochastic Analysis, Path Integration, and Dynamics , vol.200 , pp. 1-21
    • Albeverio, S.1    Röckner, M.2
  • 25
    • 0142056118 scopus 로고    scopus 로고
    • Infinite dimensional Stochastic differential equations obtained by subordination and related Dirichlet forms
    • S. Albeverio and B. Rüdiger, Infinite dimensional Stochastic differential equations obtained by subordination and related Dirichlet forms, J. Funct. Anal. 204:122-156 (2003).
    • (2003) J. Funct. Anal. , vol.204 , pp. 122-156
    • Albeverio, S.1    Rüdiger, B.2
  • 27
    • 36449000276 scopus 로고
    • Abelian Chern-Simons theory and linking numbers via oscillatory integrals
    • S. Albeverio and J. Schäfer, Abelian Chern-Simons theory and linking numbers via oscillatory integrals, J. Math. Phys. 36:2157-2169 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 2157-2169
    • Albeverio, S.1    Schäfer, J.2
  • 28
    • 0039918036 scopus 로고    scopus 로고
    • A mathematical construction of the non-Abelian Chern-Simons functional integral
    • S. Albeverio and A. Sengupta, A mathematical construction of the non-Abelian Chern-Simons functional integral, Comm. Math. Phys. 186:563-579 (1997).
    • (1997) Comm. Math. Phys. , vol.186 , pp. 563-579
    • Albeverio, S.1    Sengupta, A.2
  • 29
    • 0011436275 scopus 로고
    • L'équation de Schrödinger quand h tend vers zéro: Une approche probabiliste
    • (Marseille), Lecture Notes in Math., (Springer, Berlin)
    • R. Azencott and H. Doss, L'équation de Schrödinger quand h tend vers zéro: Une approche probabiliste (French) [The Schrödinger equation as h tends to zero: A probabilistic approach], in Stochastic Aspects of Classical and Quantum Systems (Marseille, 1983), Lecture Notes in Math., Vol. 1109 (Springer, Berlin, 1985), pp. 1-17.
    • (1983) Stochastic Aspects of Classical and Quantum Systems , vol.1109 , pp. 1-17
    • Azencott, R.1    Doss, H.2
  • 30
    • 0001295195 scopus 로고
    • A new wave equation for a continuous nondemolition measurement
    • V. P. Belavkin, A new wave equation for a continuous nondemolition measurement, Phys. Lett. A 140:355-358 (1989).
    • (1989) Phys. Lett. A , vol.140 , pp. 355-358
    • Belavkin, V.P.1
  • 31
    • 0030577873 scopus 로고    scopus 로고
    • A probabilistic approach to semi-classical approximations
    • G. Ben Arous and F. Castell, A probabilistic approach to semi-classical approximations, J. Funct. Anal. 137:243-280 (1996).
    • (1996) J. Funct. Anal. , vol.137 , pp. 243-280
    • Ben Arous, G.1    Castell, F.2
  • 32
    • 0040348025 scopus 로고
    • Stochastic quantization, stochastic calculus, and path integrals: Selected topics
    • L. Bertini, G. Jona-Lasinio, and C. Parrinello, Stochastic quantization, stochastic calculus, and path integrals: Selected topics, Progr. Theoret. Phys. Suppl. 111:83-113 (1993).
    • (1993) Progr. Theoret. Phys. Suppl. , vol.111 , pp. 83-113
    • Bertini, L.1    Jona-Lasinio, G.2    Parrinello, C.3
  • 33
    • 85171876123 scopus 로고
    • A family of integrals serving to connect the Wiener and Feynman integrals
    • R. H. Cameron, A family of integrals serving to connect the Wiener and Feynman integrals, J. Math. Phys. 39:126-140 (1960).
    • (1960) J. Math. Phys. , vol.39 , pp. 126-140
    • Cameron, R.H.1
  • 35
    • 84968509669 scopus 로고
    • Conditional analytic Feynman integrals on Wiener spaces
    • D. M. Chung, Conditional analytic Feynman integrals on Wiener spaces, Proc. AMS 112:479-488 (1991).
    • (1991) Proc. AMS , vol.112 , pp. 479-488
    • Chung, D.M.1
  • 37
    • 3543072254 scopus 로고
    • Bernstein processes associated with a Markov process
    • (Santiago), Trends. Math. (Birkhäuser Boston, Boston, MA)
    • A. B. Cruzeiro, L. Wu, and J. C. Zambrini, Bernstein processes associated with a Markov process, in Stochastic Analysis and Mathematical Physics (Santiago, 1988), Trends. Math. (Birkhäuser Boston, Boston, MA, 2000), pp. 41-72.
    • (1988) Stochastic Analysis and Mathematical Physics , pp. 41-72
    • Cruzeiro, A.B.1    Wu, L.2    Zambrini, J.C.3
  • 38
    • 0000582276 scopus 로고
    • Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians II
    • I. Daubechies and J. R. Klauder, Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians II, J. Math. Phys. 26:2239-2256 (1985).
    • (1985) J. Math. Phys. , vol.26 , pp. 2239-2256
    • Daubechies, I.1    Klauder, J.R.2
  • 40
    • 33645072536 scopus 로고
    • The Feynman integrand as a Hida distribution
    • M. De Faria, H. H. Kuo, and L. Streit, The Feynman integrand as a Hida distribution, J. Math. Phys. 32:2123-2127 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 2123-2127
    • De Faria, M.1    Kuo, H.H.2    Streit, L.3
  • 41
    • 0000915123 scopus 로고
    • Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques
    • H. Doss, Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques, Comm. Math. Phys. 73:247-264 (1980).
    • (1980) Comm. Math. Phys. , vol.73 , pp. 247-264
    • Doss, H.1
  • 42
    • 0000965484 scopus 로고
    • Feynman maps, Cameron-Martin formulae, and anharmonic oscillators
    • D. Elworthy and A. Truman, Feynman maps, Cameron-Martin formulae, and anharmonic oscillators, Ann. Inst. H. Poincaré Phys. Théor. 41:115-142 (1984).
    • (1984) Ann. Inst. H. Poincaré Phys. Théor. , vol.41 , pp. 115-142
    • Elworthy, D.1    Truman, A.2
  • 51
    • 0000010533 scopus 로고
    • Generalized uniform complex measures in the Hilbertian metric space with their applications to the Feynman path integral
    • Part 1 (California University Press, Berkeley)
    • K. Ito, Generalized uniform complex measures in the Hilbertian metric space with their applications to the Feynman path integral, Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, Part 1 (California University Press, Berkeley, 1967), pp. 145-161.
    • (1967) Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability , vol.2 , pp. 145-161
    • Ito, K.1
  • 53
    • 3543148320 scopus 로고    scopus 로고
    • Invariant measures under Schrödinger evolution and quantum statistical mechanics
    • CMS Conf. Proc., (Amer. Math. Soc., Providence, RI)
    • G. Jona-Lasinio, Invariant measures under Schrödinger evolution and quantum statistical mechanics, in Stochastic Processes, Physics, and Geometry: New Interplays, I (Leipzig, 1999), CMS Conf. Proc., Vol. 28 (Amer. Math. Soc., Providence, RI, 2000), pp. 239-242.
    • (2000) Stochastic Processes, Physics, and Geometry: New Interplays, I (Leipzig, 1999) , vol.28 , pp. 239-242
    • Jona-Lasinio, G.1
  • 54
    • 85204070999 scopus 로고
    • Stochastic processes and quantum mechanics
    • (Palaiseau), Astérisques
    • G. Jona-Lasinio, Stochastic processes and quantum mechanics, Colloquium in Honor of Laurent Schwartz, Vol. 2 (Palaiseau, 1983), Astérisques, No. 132 (1985), pp. 203-216.
    • (1983) Colloquium in Honor of Laurent Schwartz , vol.2-132 , pp. 203-216
    • Jona-Lasinio, G.1
  • 56
    • 0000945929 scopus 로고
    • On the stochastic quantization of field theory
    • G. Jona-Lasinio and P. K. Mitter, On the stochastic quantization of field theory, Comm. Math. Phys. 101:409-436 (1985).
    • (1985) Comm. Math. Phys. , vol.101 , pp. 409-436
    • Jona-Lasinio, G.1    Mitter, P.K.2
  • 58
    • 0038952850 scopus 로고
    • On a class of stochastic reaction-diffusion equations in two space dimensions
    • G. Jona-Lasinio and R. Sénéor, On a class of stochastic reaction-diffusion equations in two space dimensions, J. Phys. A 24:4123-4128 (1991).
    • (1991) J. Phys. A , vol.24 , pp. 4123-4128
    • Jona-Lasinio, G.1    Sénéor, R.2
  • 59
    • 0039862402 scopus 로고    scopus 로고
    • Study of stochastic differential equations by constructive methods I
    • G. Jona-Lasinio and R. Sénéor, Study of stochastic differential equations by constructive methods I, J. Stat. Phys. 83:1109-1148 (1996).
    • (1996) J. Stat. Phys. , vol.83 , pp. 1109-1148
    • Jona-Lasinio, G.1    Sénéor, R.2
  • 60
    • 0001507237 scopus 로고
    • Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin Formula
    • G. Kallianpur, D. Kannan, and R. L. Karandikar, Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin Formula, Ann. Inst. H. Poincaré, Prob. Th. 21:323-361 (1985).
    • (1985) Ann. Inst. H. Poincaré, Prob. Th. , vol.21 , pp. 323-361
    • Kallianpur, G.1    Kannan, D.2    Karandikar, R.L.3
  • 61
    • 0032335641 scopus 로고    scopus 로고
    • Feynman integrals for a class of exponentially growing potentials
    • T. Kuna, L. Streit, and W. Westerkamp, Feynman integrals for a class of exponentially growing potentials, J. Math. Phys. 39:4476-4491 (1998).
    • (1998) J. Math. Phys. , vol.39 , pp. 4476-4491
    • Kuna, T.1    Streit, L.2    Westerkamp, W.3
  • 62
    • 0003225839 scopus 로고
    • Lecture Notes in Math. (Springer-Verlag, Berlin/Heidelberg/New York
    • H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. (Springer-Verlag, Berlin/Heidelberg/New York, 1975).
    • (1975) Gaussian Measures in Banach Spaces
    • Kuo, H.H.1
  • 63
    • 0038867228 scopus 로고    scopus 로고
    • A rigorous construction of Abelian Chern-Simons path integrals using white noise analysis
    • S. Leukert and J. Schäfer, A rigorous construction of Abelian Chern-Simons path integrals using white noise analysis, Rev. Math. Phys. 8:445-456 (1996).
    • (1996) Rev. Math. Phys. , vol.8 , pp. 445-456
    • Leukert, S.1    Schäfer, J.2
  • 64
    • 3543058152 scopus 로고
    • Some remarks on various definitions of Feynman integrals
    • K. Jacob Beck, ed.
    • V. Mandrekar, Some remarks on various definitions of Feynman integrals, in Lectures Notes in Math., K. Jacob Beck, ed. (1983), pp. 170-177.
    • (1983) Lectures Notes in Math. , pp. 170-177
    • Mandrekar, V.1
  • 67
    • 0000431067 scopus 로고
    • Feynman integrals and the Schrödinger equation
    • E. Nelson, Feynman integrals and the Schrödinger equation, J. Math. Phys. 5:332-343 (1964).
    • (1964) J. Math. Phys. , vol.5 , pp. 332-343
    • Nelson, E.1
  • 68
    • 0011306083 scopus 로고
    • The method of stationary phase for oscillatory integrals on Hilbert spaces
    • J. Rezende, The method of stationary phase for oscillatory integrals on Hilbert spaces, Comm. Math. Phys. 101:187-206 (1985).
    • (1985) Comm. Math. Phys. , vol.101 , pp. 187-206
    • Rezende, J.1
  • 71
    • 0003845764 scopus 로고    scopus 로고
    • Princeton Series in Physics (Princeton University Press, Princeton, NJ)
    • 2 Euclidean (Quantum) Field Theory, Princeton Series in Physics (Princeton University Press, Princeton, NJ).
    • 2 Euclidean (Quantum) Field Theory
    • Simon, B.1
  • 73
    • 84888930976 scopus 로고    scopus 로고
    • Solution of Schrödinger equations on compact Lie groups via probabilistic methods
    • to appear
    • H. Thaler, Solution of Schrödinger equations on compact Lie groups via probabilistic methods, to appear in Potential Analysis.
    • Potential Analysis
    • Thaler, H.1
  • 74
    • 0009889410 scopus 로고
    • The Feynman maps and the Wiener integral
    • A. Truman, The Feynman maps and the Wiener integral, J. Math. Phys. 19:1742-1750 (1978).
    • (1978) J. Math. Phys. , vol.19 , pp. 1742-1750
    • Truman, A.1
  • 75
    • 0000368357 scopus 로고    scopus 로고
    • Smoothness and non-smoothness of the fundamental solution of time dependent Schrödiger equations
    • K. Yajima, Smoothness and non-smoothness of the fundamental solution of time dependent Schrödiger equations, Comm. Math. Phys. 181:605-629 (1996).
    • (1996) Comm. Math. Phys. , vol.181 , pp. 605-629
    • Yajima, K.1
  • 76
    • 0037906862 scopus 로고    scopus 로고
    • Feynman integrals, diffusion processes and quantum symplectic two-forms
    • J. C. Zambrini, Feynman integrals, diffusion processes and quantum symplectic two-forms, J. Korean Math. Soc. 38:385-408 (2001).
    • (2001) J. Korean Math. Soc. , vol.38 , pp. 385-408
    • Zambrini, J.C.1


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