A REGULARIZATION OF QUANTUM-FIELD HAMILTONIANS WITH THE AID OF P-ADICNUMBERS

Gaussian distributions on infinite-dimensional p-adic spaces are intro duced and the corresponding L-2-spaces of p-adic-valued square integra ble functions are constructed. Representations of the infinite-dimensi onal Weyl group are realized in p-adic L-2-spaces. There is a formal a nalogy with the usual Segal representation. But there is also a large topological difference: parameters of the p-adic infinite-dimensional Weyl group are defined only on some balls (these balls are additive su bgroups). p-adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constru cted. Many Hamiltonians with potentials which are too singular to exis t as functions over reals are realized as bounded symmetric operators in L-2-spaces with respect to a p-adic Gaussian distribution.