Unifying the theory of Integration within normal-, Weyl- and antinormal-ordering of operators and the s--ordered operator expansion formula of density operators

TL;DR

This paper introduces a unified framework for operator integration in phase-space quantum mechanics, encompassing normal, Weyl, and antinormal orderings through an s-parameterized approach, and derives a comprehensive operator expansion formula.

Contribution

It develops a generalized integration technique within s-ordered products, unifying various operator orderings and establishing a complete s-parameterized quantization scheme.

Findings

Derived the s-parameterized operator expansion formula for density operators.

Unified the treatment of normal, Weyl, and antinormal orderings.

Established a complete s-parameterized quantization scheme.

Abstract

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normal ordered, antinormally ordered and Weyl ordered product of operators as its special cases). The s-ordered operator expansion formula of density operators is derived, and the s-parameterized quantization scheme is thus completely established.