谱的算术：分解、统计与对称函数
The Arithmetic of Spectra: Factorization, Statistics, and Symmetric Functions
- Hendrix Industries（亨德里克斯工业公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过谱字母和对称函数方法，系统研究无相互作用量子系统单粒子谱的分解，并建立规范玻色与费米配分函数的统一组合框架。
AI中文摘要：
我们研究了无相互作用量子系统单粒子谱的分解及其对多粒子统计的影响。通过用谱字母表示单粒子配分函数，张量分解变为字母的乘法分解，并利用标准对称函数和λ-环恒等式将其提升为规范玻色和费米配分函数。我们展示了乘积谱如何由不同分解产生，反对称化如何在奇数个因子间分配，以及哪些张量分解与固定谱兼容。因此，本文研究了谱分解，并为规范玻色和费米配分函数提供了一个统一的组合框架。
英文摘要：
We study factorizations of the single-particle spectrum of non-interacting quantum systems and their consequences for many-particle statistics. Representing the single-particle partition function by a spectral alphabet, tensor factorizations become multiplicative factorizations of the alphabet, which can be lifted to canonical Bose and Fermi partition functions using standard symmetric-function and $λ$-ring identities. We show how product spectra arise from different factorizations, how antisymmetrization can be assigned across an odd number of factors, and which tensor factorizations are compatible with a fixed spectrum. The paper therefore studies spectral factorization and provides a consolidated combinatorial framework for canonical Bose and Fermi partition functions.
