Approximate substitutions and the normal ordering problem

TL;DR

This paper introduces a novel approach to the normal ordering problem in quantum mechanics by representing infinite generalized Stirling matrices as projective limits of finite algebraic systems called approximate substitutions.

Contribution

It establishes a new connection between the normal ordering problem and algebraic structures called approximate substitutions, providing a finite algebraic characterization.

Findings

Infinite generalized Stirling matrices are projective limits of approximate substitutions.

Approximate substitutions are characterized by finite algebraic equations.

The approach offers a new algebraic perspective on the normal ordering problem.

Abstract

In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations.