Negative Power Spectra in Quantum Field Theory

TL;DR

This paper explores the phenomenon of negative power spectra in quantum field theory, challenging traditional positivity assumptions and discussing implications for cosmology.

Contribution

It demonstrates that quadratic operator fluctuations can have negative power spectra, explaining the failure of the Wiener-Khinchine theorem in this context.

Findings

Power spectra of quadratic operators can be negative.

Standard positivity arguments do not apply to these spectra.

Potential implications for cosmological models.

Abstract

We consider the spatial power spectra associated with fluctuations of quadratic operators in field theory, such as quantum stress tensor components. We show that the power spectrum can be negative, in contrast to most fluctuation phenomena where the Wiener-Khinchine theorem requires a positive power spectrum. We show why the usual argument for positivity fails in this case, and discuss the physical interpretation of negative power spectra. Possible applications to cosmology are discussed.