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arXiv · 2602.00920

A structural criterion for asymptotic states in Supersymmetry

Stefano Bellucci·Stefania De Matteo
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Abstract

The occurrence of a field in the formal structure of a quantum field theory does not by itself establish the existence of a corresponding asymptotic particle. We develop a structural criterion separating three logically distinct questions: which field structures are admissible, which survive the dynamics as localized spectral excitations, and which are realized as operational particle states. The revised exterior-polynomial classification of gravitino mass bilinears provides the operator-level prototype for this distinction. Transposing this layered logic from operators to states, we formulate particlehood as the endpoint of an ordered filtration: spacetime geometry and the quantum state determine the spectral environment; the effective algebra fixes the physically realized symmetries and admissible channels; dynamics modifies the dressed two-point function; and spectral analysis determines whether an isolated atomic contribution survives. The localization criterion is thereby given measure-theoretic content: a stable asymptotic particle state requires an isolated spectral atom with non-zero weight. The framework also clarifies two limits of the original formulation. The apparent fermion-scalar asymmetry is channel-specific rather than universal, and no asymmetric realization of particlehood within an exact supersymmetric multiplet is possible while the supercharges act on the physical Hilbert space and annihilate the vacuum. Any split therefore requires supersymmetry breaking, altered background realization, or kinematic and dynamical differences among the relevant channels. The paper establishes necessary structural conditions only; their quantitative realization is deferred to a companion work.

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Stefano Bellucci, Stefania De Matteo. 2026-01-31. A structural criterion for asymptotic states in Supersymmetry. https://arxiv.org/abs/2602.00920

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