Convergence of Infinite Series in Bosonic Second Quantization

TL;DR

This paper investigates the convergence of infinite series in bosonic second quantization, establishing conditions for convergence and analyzing properties of the resulting operators in bosonic Fock space.

Contribution

It provides a rigorous analysis of the domain of convergence for series defining second quantization and quadratic operators in bosonic Fock space, using number operator estimates and functional analysis tools.

Findings

Identifies conditions for convergence of series in bosonic second quantization.

Derives fundamental properties of the limit operators in the Fock space.

Establishes the domain of these operators through precise estimates.

Abstract

The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator estimates and the Banach-Steinhaus Theorem. Some fundamental properties of the limit operators are derived.