A structural criterion for asymptotic states in Supersymmetry

TL;DR

This paper introduces a structural criterion to distinguish algebraically allowed degrees of freedom from those forming stable asymptotic states in supersymmetric quantum field theories, highlighting differences between fermionic and scalar fields.

Contribution

It proposes a minimal, background fluctuation-based localization criterion that is independent of specific dynamics or interactions, clarifying conditions for particle existence in supersymmetry.

Findings

Fermionic modes can remain stable under structural fluctuations.

Scalar modes generally decohere and do not form localized states.

The criterion is model-independent and does not rely on supersymmetry-breaking mechanisms.

Abstract

In quantum field theory, the algebraic existence of a field does not guarantee the existence of a corresponding localized asymptotic particle state. This distinction is well established in the presence of infrared effects, long-range correlations, and environmental interactions, and becomes particularly relevant in supersymmetric theories, where fermionic and bosonic degrees of freedom are constrained at the algebraic level but need not share identical asymptotic behavior. In this work we introduce a minimal and predynamical localization criterion that distinguishes algebraically allowed degrees of freedom from those capable of forming stable, phasecoherent asymptotic states. The criterion is formulated in terms of long-time stability under slow structural fluctuations of an effective background, without modifying the underlying field equations or introducing new physical interactions. We show that fermionic and scalar fields respond qualitatively differently to such structural effects. While fermionic modes may retain asymptotic stability, scalar modes generically exhibit decoherence and damping, preventing their interpretation as localized one-particle states. This provides a conservative and model-independent perspective on how supersymmetric algebraic structures may coexist with an asymmetric observable particle spectrum. The analysis is intentionally non-constructive and does not rely on specific supersymmetrybreaking mechanisms, cosmological assumptions, or new dynamical ingredients. Rather, it clarifies localization as an independent structural requirement for particle existence within standard quantum field theory.