Creator-annihilator domains and the number operator

TL;DR

This paper investigates the domain properties of creators, annihilators, and the number operator in infinite-dimensional bosonic Fock space, revealing that the maximal common domain of creators and annihilators is larger than that of the square-root of the number operator.

Contribution

It establishes a precise relationship between the domains of creators, annihilators, and the number operator in infinite-dimensional bosonic Fock space.

Findings

Maximal common domain of creators and annihilators exceeds the domain of the square-root of the number operator.

Provides insight into the domain structure of operators in infinite-dimensional quantum systems.

Enhances understanding of operator domains in quantum field theory.

Abstract

We show that for the bosonic Fock representation in infinite dimensions, the maximal common domain of all creators and annihilators properly contains the domain of the square-root of the number operator.