# 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.

## Key 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.