On the vacuum in the Moyal quantization

TL;DR

This paper investigates the properties of the harmonic oscillator vacuum in Moyal quantization, comparing normal and Weyl orderings and discussing their differences and implications.

Contribution

It provides a detailed comparison between normal ordered and Weyl ordered vacuums in Moyal quantization, highlighting their differences and physical implications.

Findings

Weyl ordered vacuum expressed explicitly

Differences between normal and Weyl ordered vacuums analyzed

Implications of ordering choices discussed

Abstract

We study the features of the vacuum of the harmonic oscillator in the Moyal quantization. The vacuums with and without using the normal ordering look different. The vacuum without the normal ordering is shown to be expressed using the Weyl ordering. The Weyl ordered vacuum is then compared with the normal ordered vacuum, and the implication of the difference between them is discussed.