副粒子本质上表现出哈代空间崩溃
Paraparticles intrinsically exhibit Hardy-space breakdown
中文总结 AI 辅助
研究副粒子非酉交换统计对哈代空间解析性的破坏，通过分析记忆核、度量η等，发现副粒子耦合时会打破标准色散关系，费米子和玻色子不受影响，此内在违反在记忆核解析结构层面区分了不同统计。
中文摘要 AI 辅助
开放量子系统的记忆核当且仅当其拉普拉斯变换在上半平面解析时才服从克拉默斯 - 克朗尼格（KK）关系，这一性质称为哈代空间解析性。本文表明，作为副粒子定义属性的非酉交换统计本质上破坏了哈代空间解析性。保证这些粒子实封闭系统谱的度量η必然不同于物理的玻恩内积（\(\|\eta - I\|_F / \|I\|_F = 0.51\)），这是R矩阵非酉性的数学结果而非参数选择。该度量是一种“影子度量”，在封闭系统中物理上不可见。但当副粒子与浴耦合时，任何位于对称代数之外的耦合算符会暴露这种扭曲。记忆核在耦合\(g_c \approx 0.1\)处出现上半平面极点，在封闭系统谱复化之前就打破了标准色散关系。费米子和玻色子由于交换是酉的而不受影响。这种违反是内在的，它在记忆核解析结构层面区分了非酉交换统计与普通粒子统计。
英文摘要
The memory kernel of an open quantum system obeys Kramers--Kronig (KK) relations if and only if its Laplace transform is analytic in the upper half-plane -- a property known as Hardy-space analyticity. Here we show that non-unitary exchange statistics, the defining property of paraparticles, intrinsically breaks Hardy-space analyticity. The metric $η$ that guarantees a real closed-system spectrum for these particles necessarily differs from the physical Born inner product ($\|η- I\|_F / \|I\|_F = 0.51$) -- a mathematical consequence of the R-matrix's non-unitarity, not a parameter choice. This metric is a "shadow metric": Schur's lemma forces it to commute with every bilinear observable, making the distortion physically invisible in the closed system. But when the paraparticle is coupled to a bath, any coupling operator that lies outside the symmetry algebra -- that is, any interaction that sees the internal flavour structure -- exposes the distortion. The memory kernel then develops upper-half-plane poles at coupling $g_c \approx 0.1$, breaking standard dispersion relations before the closed-system spectrum complexifies. Fermions and bosons, whose exchange is unitary ($η= I$ as an analytic fact of the canonical anticommutation algebra), are immune at any coupling, because there is no distortion to expose. The violation is intrinsic: it distinguishes non-unitary exchange statistics from ordinary particle statistics at the level of the memory kernel's analytic structure.
