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

TL;DR

This paper explores the structure of free coherent states within rigged Hilbert spaces, establishing an isomorphism to p-adic function spaces and connecting noncommutative geometry with p-adic analysis.

Contribution

It demonstrates a novel isomorphism between rigged Hilbert spaces of free coherent states and spaces of generalized functions on p-adic disks, linking noncommutative geometry with p-adic numbers.

Findings

Rigged Hilbert space of free coherent states is isomorphic to p-adic function space.

The work connects noncommutative geometry with p-adic analysis.

Provides a new perspective on the mathematical structure of quantum states.

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.