Abstract
Existence theorems and evaluation formulas are obtained for the analytic Feynman integral corresponding to functionals of the form given below in (1.1).
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References
ALBEVERIO, A. and R. HOEGH-KROHN: Mathematical theory of Feynman path integrals, Lecture Notes in Mathematics 523, Springer-Verlag, Heidelberg-Berlin-New York 1976.
ALBEVERIO, A. and R. HOEGH-KROHN: ‘Feynman path integrals and the corresponding method of stationary phase, Feynman path integrals’, Lecture Notes in Physics 106, Springer-Verlag, Berlin-Heidelberg-New York 1979, 3–57.
CAMERON, R.H. and D.A. STORVICK: ‘Some Banach algebras of analytic Feynman integrable functionals’ in: Proceedings, Analytic Functions, Kozubnik 1979, ed. by J. Ławrynowicz, Lecture Notes in Mathematics 798, Springer-Verlag, Berlin-Heidelberg-New York 1980, 18–67.
CAMERON, R.H. and D.A. STORVICK: ‘Analytic Feynman integral solutions of an integral equation related to the Schrödinger equation’, J. Analyse Math. 38 (1980), 34–66.
CAMERON, R.H. and D.A. STORVICK: ‘A new translation theorem for the analytic Feynman integral’, Rev. Roum. Math. Pures et Appl. 27,9 (1982), 937–944.
CAMERON, R.H. and D.A. STORVICK: ‘A simple definition of the Feynman integral, with applications’, Mem. Amer. Math. Soc. 46,288 (1983).
CAMERON, R.H. and D.A. STORVICK: ‘New existence theorems and evaluation formulas for sequential Feynman integrals’, Proc, London Math Soc. (3) 52 (1986), 557–581.
ELWORTHY, D. and A. TRUMAN: ‘A Cameron-Martin formula for Feynman integrals’, in: Mathematical problems in theoretical physics, Lecture Notes in Physics 153, Springer-Verlag, Berlin-Heidelberg-New York 1981, 288–294.
FEYNMAN, R.P.: ‘Space-time approach to non-relativistic quantum mechanics’, Rev. Mod. Phys. 20 (1948), 367–387.
JOHNSON, G.W. and D. SKOUG: ‘Notes on the Feynman integral, III: the Schrödinger equation’, Pacific J. Math. 105 (1983), 321–358.
PALEY, R.E.A.C., N. WIENER and A. ZYGMUND: ‘Notes on random functions’, Math. Z. 37 (1933), 647–688.
TRUMAN, A.: ‘The Feynman maps and the Wiener integral’, J. Math. Phys. 19,8 (1978).
TRUMAN, A.: ‘The polygonal path formulation of the Feynman path integral’ in: Feynman path integrals, Lecture Notes in Physics 106, Springer-Verlag, Berlin-Heidelberg-New York 1979, 73–102.
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© 1989 Kluwer Academic Publishers
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Cameron, R.H., Storvick, D.A. (1989). New Existence Theorems and Evaluation Formulas for Analytic Feynman Integrals. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_27
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DOI: https://doi.org/10.1007/978-94-009-2643-1_27
Publisher Name: Springer, Dordrecht
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