Geodesic
Generalized functions and Gaussian path integrals over non-archimedean function spaces
Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 761-794

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A mathematical apparatus is developed for non-Archimedean physics: a theory of generalized functions, a theory of integration, and a harmonic analysis. Both finite-dimensional and infinite-dimensional non-Archimedean spaces are considered. Gaussian and Feynman path integrals on non-Archimedean function spaces are introduced. Quantization of a non-Archimedean scalar bosonic field is carried out in the formalism of path integrals. Linear differential equations in spaces of test functions and spaces of generalized functions on infinite-dimensional non-Archimedean spaces are studied (in particular, the heat equation and the Schrödinger equation with a potential). 
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     author = {A. Yu. Khrennikov},
     title = {Generalized functions and {Gaussian} path integrals over non-archimedean function spaces},
     journal = {Izvestiya. Mathematics },
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     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a3/}
}
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A. Yu. Khrennikov. Generalized functions and Gaussian path integrals over non-archimedean function spaces. Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 761-794. http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a3/