Feynman integrals as Hida distributions: the case of non-perturbative potentials
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque no. 327  (2009), p. 55-68
@incollection{AST_2009__327__55_0,
     author = {Grothaus, Martin and Streit, Ludwig and Vogel, Anna},
     title = {Feynman integrals as Hida distributions: the case of non-perturbative potentials},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     pages = {55-68},
     zbl = {1200.60056},
     mrnumber = {2642352},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__55_0}
}
Grothaus, Martin; Streit, Ludwig; Vogel, Anna. Feynman integrals as Hida distributions: the case of non-perturbative potentials, in From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 55-68. http://www.numdam.org/item/AST_2009__327__55_0/

[1] Y. Berezansky & Y. G. Kondratiev - Spectral methods in infinite-dimensional analysis, Kluwer Academic, 1995, originally in Russian, Naukova Dumka, Kiev, 1988. | Article | MR 978630 | Zbl 0832.47001

[2] C. C. Bernido & M. V. Carpio-Bernido - "Path integrals for boundaries and topological constraints: a white noise functional approach", J. Math. Phys. 43 (2002), p. 1728-1736. | Article | MR 1892750 | Zbl 1059.81108

[3] R. H. Cameron - "A family of integrals serving to connect the Wiener and Feynman integrals", J. Math, and Phys. 39 (1960/1961), p. 126-140. | Article | MR 127776 | Zbl 0096.06901

[4] H. Doss - "Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques", Comm. Math. Phys. 73 (1980), p. 247-264. | Article | MR 574173 | Zbl 0427.60099

[5] M. De Faria, M. J. Oliveira & L. Streit - "Feynman integrals for nonsmooth and rapidly growing potentials", J. Math. Phys. 46 (2005), 063505. | Article | MR 2149846 | Zbl 1110.81130

[6] M. De Faria, J. Potthoff & L. Streit - "The Feynman integrand as a Hida distribution", J. Math. Phys. 32 (1991), p. 2123-2127. | Article | MR 1123604 | Zbl 0754.46050

[7] M. Grothaus, D. C. Khandekar, J. L. Da Silva & L. Streit - "The Feynman integral for time-dependent anharmonic oscillators", J. Math. Phys. 38 (1997), p. 3278-3299. | Article | MR 1449564 | Zbl 0878.58011

[8] M. Grothaus & A. Vogel - "The Feynman integrand as a white noise distribution beyond pertubation theory", in Stochastic and quantum dynamics of biomolecular systems. Proceedings of the 5th Jagna international workshop, Jagna, Bohol, Philippines, 3-5 January 2008. Melville, NY: American Institute of Physics (C. Bernido et al., eds.), AIP Conference Proceedings, vol. 1021, 2008, p. 25-33. | Zbl 1156.81420

[9] T. Hida - Brownian motion, Applications of Mathematics, vol. 11, Springer, 1980. | MR 562914 | Zbl 0432.60002

[10] T. Hida, H.-H. Kuo, J. Potthoff & L. Streit - White noise, Mathematics and its Applications, vol. 253, Kluwer Academic Publishers Group, 1993. | MR 1244577 | Zbl 0771.60048

[11] D. C. Khandekar & L. Streit - "Constructing the Feynman integrand", Ann. Physik 1 (1992), p. 49-55. | Article | MR 1161912

[12] Y. G. Kondratiev, P. Leukert, J. Potthoff, L. Streit & W. Westerkamp - "Generalized functionals in Gaussian spaces: the characterization theorem revisited", J. Funct. Anal 141 (1996), p. 301-318. | Article | MR 1418508 | Zbl 0871.60033

[13] T. Kuna, L. Streit & W. Westerkamp - "Feynman integrals for a class of exponentially growing potentials", J. Math. Phys. 39 (1998), p. 4476-4491. | Article | MR 1643273 | Zbl 0934.58014

[14] H.-H. Kuo - White noise distribution theory, Probability and Stochastics Series, CRC Press, 1996. | MR 1387829 | Zbl 0853.60001

[15] R. Leandre - "Path integrals in non-commutative geometry", in Encyclopedia of Mathematical Physics, Academic Press/Elsevier Science, 2006, p. 8-12. | Article

[16] J. Potthoff - "Introduction to white noise analysis", in Control theory, stochastic analysis and applications (Hangzhou, 1991), World Sci. Publ., River Edge, NJ, 1991, p. 39-58. | MR 1171663

[17] J. L. Silva & L. Streit - "Feynman integrals and white noise analysis", in Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002), World Sci. Publ., River Edge, NJ, 2004, p. 285-303. | Article | MR 2115942