超对称中渐近态的结构判据
A structural criterion for asymptotic states in Supersymmetry
AI总结：
本文提出了一种超对称中渐近态的结构判据，区分代数允许的自由度与能形成稳定渐近态的自由度，揭示费米子与标量场在结构效应下的不同响应。
摘要：
在量子场论中，一个场的代数存在性并不保证存在相应的局部渐近粒子态。这种区别在存在红外效应、长程相关性和环境相互作用的情况下已被充分确立，并在超对称理论中变得尤为重要，其中费米子和玻色子自由度在代数层面受到限制，但不一定具有相同的渐近行为。在本工作中，我们引入了一个最小且预动力学的局部化判据，以区分代数允许的自由度与能够形成稳定、相协调渐近态的自由度。该判据以有效背景的长时间稳定性在缓慢结构波动下进行表述，而不修改基本场方程或引入新的物理相互作用。我们展示出费米子和标量场对这种结构效应的反应存在定性差异。虽然费米子模式可能保持渐近稳定性，但标量模式通常表现出退相干和阻尼，阻碍其被解释为局部单粒子态。这为超对称代数结构如何与不对称可观测量粒子谱共存提供了保守且模型无关的视角。分析是故意非构造性的，并不依赖于特定的超对称破缺机制、宇宙学假设或新的动力学成分。相反，它澄清了局部化作为标准量子场论中粒子存在的独立结构要求。
英文摘要：
The occurrence of a field in a quantum field theory does not by itself establish the existence of a corresponding asymptotic particle. We formulate a structural criterion separating operator admissibility, dynamical spectral realization, and particlehood, using the exterior-polynomial classification of gravitino mass bilinears as a prototype. Particlehood is organized as an ordered filtration of geometry and state, effective algebra, dynamics, and spectral analysis, with the localization criterion $Λ[Ψ]$ defined by the presence of a physical spectral atom of non-zero weight. We obtain four results. First, conventional linearly realized global supercharges are obstructed on a positive-definite de Sitter Hilbert space when the full diagonal odd--odd bracket satisfies a positivity-reversal condition; the spacetime part is shown to be reversible in $\mathfrak{so}(4,1)$, while internal generators require a separate check. Second, invariant scalar de Sitter product decompositions remove the Minkowski additive two-particle threshold in principal-series channels. Third, a spectral-transfer decomposition shows how continuum weight in a mediator propagator can open absorptive support for an external field below the atomic mediator threshold. Fourth, in a reduced effective-operator basis, the fermionic vector derivative coupling is redundant under current-conservation assumptions, whereas the axial dimension-five coupling is physical unless excluded by parity or CP; under that symmetry hypothesis the residual fermionic derivative potential starts one operator dimension above the scalar one. Exact unbroken supersymmetry enforces multiplet rigidity of the atomic criterion.
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