The Arithmetic of Spectra: Factorization, Statistics, and Symmetric Functions
Abstract
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.
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BibTeX
@misc{chaudhary2026arithmetic,
title = {{The Arithmetic of Spectra: Factorization, Statistics, and Symmetric Functions}},
author = {A. Chaudhary},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10391},
eprint = {2609.10391},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10391},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Arithmetic of Spectra: Factorization, Statistics, and Symmetric Functions
AU - A. Chaudhary
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.10391
UR - https://arxiv.org/abs/2609.10391
AB - 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.
ER -