Rigged Hilbert space of the free coherent states and p-adic numbers

Abstract

Rigged Hilbert space of the free coherent states is investigated. We prove that this rigged Hilbert space is isomorphous to the space of generalized functions on p-adic disk. We discuss the relation of the described isomorphism of rigged Hilbert spaces and noncommutative geometry and show, that the considered example realises the isomorphism of the noncommutative line and p-adic disk.