On Polynomial Relations in the Heisenberg Algebra

TL;DR

This paper explores polynomial relations within the Heisenberg algebra, linking classical and quantum forms, and discusses their implications for normal ordering in quantum mechanics.

Contribution

It introduces polynomial relations in the Heisenberg algebra that connect classical and quantum cases, providing new insights into operator ordering.

Findings

Polynomial relations between classical and quantum Heisenberg algebra generators.

Some relations serve as formulas for normal ordering of creation/annihilation operators.

Enhances understanding of algebraic structures in quantum mechanics.

Abstract

Polynomial relations between the generators of the classical and quantum Heisenberg algebras are presented. Some of those relations can have a meaning of the formulas of the normal ordering for the creation/annihilation operators occurred in the method of the second quantization.