The Feynman integral and Feynman's operational calculus : a heuristic and mathematical introduction
Annales mathématiques Blaise Pascal, Volume 3 (1996) no. 1, pp. 89-102.
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     title = {The {Feynman} integral and {Feynman's} operational calculus : a heuristic and mathematical introduction},
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Michel L. Lapidus. The Feynman integral and Feynman's operational calculus : a heuristic and mathematical introduction. Annales mathématiques Blaise Pascal, Volume 3 (1996) no. 1, pp. 89-102. https://ambp.centre-mersenne.org/item/AMBP_1996__3_1_89_0/

[Ar]Araki, H. Expansionals in Banach algebras, Ann. Sci. Ecole Norm. Sup. 6 (1973), 67-84. | Numdam | MR | Zbl

[BaJoYo]Badrikian, A., Johnson, G.W. and Yoo Il, , The composition of operator-valued measurable functions is measurable, Proc. Amer. Math. Soc. 123 (1995), 1815-1820. | MR | Zbl

[Ca]Cameron, R.H., A family of integrals serving to connect the Wiener and Feynman integrals, J. Math and Physics 39 (1960), 126-140. | MR | Zbl

[CaSt]Cameron, R. H. and Storvick, D.A., An operator-valued function space integral and a related integral equation, J. Math. Mech. 18 (1968), 517-552. | MR | Zbl

[ChSa]Chadan, K. and Sabatier, P.C., Inverse Problems in Quantum Scattering Theory (1989), 2nd ed., Springer-Verlag, New York. | MR | Zbl

[dFJoLa1] Defacio, B., Johnson, G.W. and Lapidus, M.L., Feynman's operational calculus as a generalized path integral, in Stochastic Processes: A Festschrift in Honour of Gopinath Kallianpur, S. Cambanis et al, Springer-Verlag, New York, 1993, pp. 51-60. | MR | Zbl

[dFJoLa2] _____, Feynman's operational calculus and evolution equations. Preprint IHES/M/95/54, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France, 1995 (80 pages). (To appear in Acta Applicandae Mathematicae.) | MR

[Dy]Dyson, F.J., The radiation theories of Tomonaga, Schwinger and Feynman, Phys. Rev. 75 (1949), 486-502. | MR | Zbl

[Fe1] Feynman, R.P., Space-time approach to non-relativistic quantum mechanics, Rev. Modern Phys. 20 (1948), 367-387. | MR

[Fe2]_____, An operator calculus having applications in quantum electrodynamics, Phys. Rev. 84 (1951), 108-128. | MR | Zbl

[Gi]Gill, T.L., Time-ordered operators I, Trans. Amer. Math. Soc. 266 (1981), 161-181. | MR | Zbl

[Gi]Gill, T.L., Time-ordered operators II, Trans. Amer. Math. Soc. 289 (1983), 617-634 . | MR | Zbl

[GiZa]Gill, T. L. and Zachary, W.W., Time-ordered operators and Feynman-Dyson algebras, J. Math. Phys. 28 (1987), 1459-1470. | MR | Zbl

[GlJa]Glimm, J. and Jaffe, A., Quantum Physics: a Functional Integral Point of View, Springer-Verlag, New York, 1981. | MR | Zbl

[JeJo]Jefferies, B. and Johnson, G.W., Functional calculi for noncommuting operators, in prep.

[Jo]Johnson, G.W., The product of strong operator measurable functions is strong operator measurable, Proc. Amer. Math. Soc. 117 (1993), 1097-1104. | MR | Zbl

[JoLa1]Johnson, G.W. and Lapidus, M.L., Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operational calculus, Memoirs Amer. Math. Soc. 62 (1986), 1-78. | MR | Zbl

[JoLa2]_____, Feynman's operational caculus, generalized Dyson series and the Feynman integral, in "Operator Algebras and Mathematical Physics" P. E. T. Jorgensen and P. Muhly, Contemporary Mathematics, Vol. 62, Amer. Math. Soc., Providence, 1987, pp. 437-445. | Zbl

[JoLa3] _____, Une multiplication non commutative des fonctionnelles de Wiener et le calcul opérationnel de Feynman, C. R. Acad. Sci. Paris Sér. I Math.304 (1987), 523-526. | MR | Zbl

[JoLa4]_____, Noncommutative operations on Wiener functionals and Feynman's operational calculus, J. Funct. Anal. 81 (1988), 74-99. | MR | Zbl

[JoLa5]_____, The Feynman Integral and Feynman's Operational Calculus, Oxford Mathematical Monographs, Oxford Univ. Press, Oxford and New York, to appear. | MR | Zbl

[JoSk]Johnson, G. W. and Skoug, D.L., The Cameron- Storvick function space integral: an L(Lp, Lp,) theory, Nagoya Math. J. 60 (1976), 93-137. | MR | Zbl

[La1] Lapidus, M.L., Formule de Trotter et Calcul Cpérationnel de Feynman, Thèse de Doctorat d'Etat ès Sciences, Mathématiques. Université Pierre et Marie Curie (Paris VI), Paris, France, 1986. (Part I: Formules de Trotter et Intégrales de Feynman. Part III: Calcul Opérationnel de Feynman.)

[La2]_____, The differential equation for the Feynman-Kac Formula with a Lebesgue-Stieltjes measure, Lett. Math. Phys. 11 (1986), 1-13. | MR | Zbl

[La3]_____, The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus, Stud. Appl. Math. 76 (1987), 93-132. | MR | Zbl

[La4]_____, The Feynman-Kac formula with a Lebesgue-Stieltjes measure: an integral equation in the general case, Integral Equations Operator Theory 12 (1989), 162-210. | MR | Zbl

[La5]_____, Strong product integration of measures and the Feynman-Kac formula with a Lebesgue-Stieltjes measure, in Proc. Sherbrooke Conference on Functional Integration,Supp. Rend. Circ. Mat. Palermo, Ser. II 17 (1987), pp. 271-312. | MR | Zbl

[La6] _____, Quantification, calcul opérationnel de Feynman axiomatique et intégrale fonctionnelle généralisée, C. R. Acad. Sci. Paris Sér. I 308 (1989), 133-138. | MR | Zbl

[Ma] Maslov, V.P., Operational Methods, English transl. (Rev. from the 1973 Russian ed.), Moscow, Mir, 1976. | MR | Zbl

[McC] Mccarthy, I.E., Introduction to Nuclear Theory, Wiley and Sons, New York, 1968.

[Ne]Nelson, E., Operants: a functional calculus for non-commuting operators, in Proc. Conf. in Honor of Marshall Stone, F. E. Browder, Springer-Verlag, New York, 1970, pp. 172-187. | MR | Zbl

[Re] Reyes J.T.Thesis, Univ. of Nebraska, Lincoln, in prep.

[Si] Simon, B., Functional Integration and Quantum Physics, Academic Press, New York, 1979. | MR | Zbl

[Ta] Tabakin, F., An effective interaction for nuclear Hartree-Fock calculations, Annals Phys. (N. Y.) 30 (1964), 51-64.