小数据违规
Small Violations of Statistics
摘要：
考虑既不是玻色也不是费米的统计有两个动机：（1）扩展量子理论和量子场论的框架，（2）提供一种对可能违反统计的定量度量。在回顾了各种粒子的统计测试以及既不是玻色也不是费米的统计类型之后，我讨论了quons，即以参数$q$为特征的粒子，它允许玻色和费米统计之间的平滑插值; $q=1$给出玻色子，$q=-1$给出费米子。这次演讲的新成果是罗伯特·C. Hilborn和我给出了一个启发性的论点，将统计守恒扩展到具有$\bar{f}fb$形式的三线性耦合的量子，其中$f$是费米子类，$b$是玻色子类。我们证明了$q_f^2=q_b$ .特别是，我们将$q_γ$上的光子束缚与$q_e$上的电子束缚联系起来，使得非常精确的电子束缚可以传递给光子。我们的论证的一个扩展表明，所有粒子都是费米子或玻色子，精确度很高。
英文摘要：
There are two motivations to consider statistics that are neither Bose nor Fermi: (1) to extend the framework of quantum theory and of quantum field theory, and (2) to provide a quantitative measure of possible violations of statistics. After reviewing tests of statistics for various particles, and types of statistics that are neither Bose nor Fermi, I discuss quons, particles characterized by the parameter $q$, which permit a smooth interpolation between Bose and Fermi statistics; $q=1$ gives bosons, $q=-1$ gives fermions. The new result of this talk is work by Robert C. Hilborn and myself that gives a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form $\bar{f}fb$, where $f$ is fermion-like and $b$ is boson-like. We showed that $q_f^2=q_b$. In particular, we related the bound on $q_γ$ for photons to the bound on $q_e$ for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of our argument suggests that all particles are fermions or bosons to high precision.
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