A misleading naming convention: de Sitter `tachyonic' scalar fields

TL;DR

This paper uses a group-theoretical, Wigner-inspired framework to reexamine de Sitter scalar fields with negative squared mass, showing that such fields correspond to dS group UIRs rather than intrinsic instabilities. The Garidi mass provides a dS-invariant notion of mass that reduces to the Minkowski mass in the flat limit $H\to0$, clarifying which UIRs have a Minkowskian interpretation and when the negative-$m_H^2$ label is meaningful. It argues that instability arises from gauge anomalies and is resolved by Gupta-Bleuler (within a Krein-space setting), yielding a consistent, causal quantum field theory on de Sitter spacetime with a physical Hilbert space and positive energy in physical states. The results connect to broader issues in curved-spacetime QFT, including graviton scenarios, and underscore the importance of precise group-theoretical foundations and terminology in interpreting fields in highly symmetric spacetimes.

Abstract

We revisit the concept of de Sitter (dS) 'tachyonic' scalar fields, characterized by discrete negative squared mass values, and assess their physical significance through a rigorous Wigner-inspired group-theoretical analysis. This perspective demonstrates that such fields, often misinterpreted as inherently unstable due to their mass parameter, are best understood within the framework of unitary irreducible representations (UIRs) of the dS group. The discrete mass spectrum arises naturally in this representation framework, offering profound insights into the interplay between dS relativity and quantum field theory. Contrary to their misleading nomenclature, we argue that the 'mass' parameter associated with these fields lacks intrinsic physical relevance, challenging traditional assumptions that link it to physical instability. Instead, any perceived instability originates from mismanagement of the system's inherent gauge invariance rather than the fields themselves. A proper treatment of this gauge symmetry, particularly through the Gupta-Bleuler formalism, restores the expected characteristics of these fields as free quantum entities in a highly symmetric spacetime. This study seeks to dispel misconceptions surrounding dS 'tachyonic' fields, underscoring the importance of precise terminology and robust theoretical tools in addressing their unique properties.