ALBEVERIO AND HOEGH-KROHN APPROACH TO A P-ADIC FUNCTIONAL-INTEGRATION

The theory of p-adic valued Gaussian and Feynman integration on infini te-dimensional spaces is developed with the aid of the Albeverio and H oegh-Krohn approach based on the Fourier (or Laplace) transform of the infinite-dimensional distributions. Gaussian distributions cannot be realized as bounded p-adic valued measures and there is no difference between Gaussian and Feynman integration in this case. The free p-adic valued quantum field is realized in the space of Gaussian square inte grable functions.