Generalized functions and Gaussian path integrals over non-archimedean function spaces

A. Yu. Khrennikov

Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 761-794.

Résumé

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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