On anti-de Sitter oscillators and de Sitter anti-oscillators

TL;DR

This paper explores the interpretation of free quantum fields on anti-de Sitter and de Sitter spacetimes as oscillators or anti-oscillators, highlighting a specific de Sitter chart where the Dirac field acts as an anti-oscillator in the non-relativistic limit.

Contribution

It provides a new perspective on quantum fields in curved spacetimes, especially identifying a de Sitter chart where the Dirac field behaves as an anti-oscillator.

Findings

Quantum fields on anti-de Sitter/spacetimes can be viewed as oscillators or anti-oscillators.

A specific de Sitter chart makes the Dirac field an anti-oscillator in the non-relativistic limit.

The interpretation extends the understanding of quantum fields in curved backgrounds.

Abstract

We revisit the principal arguments for interpreting the free quantum fields on anti-de Sitter or de Sitter spacetimes of any dimensions as oscillators or respectively anti-oscillators. In addition, we point out that there exists a chart on the de Sitter background where the free Dirac field becomes a genuine anti-oscillator in the non-relativistic limit in the sense of special relativity.