PreprintCC BY-NC-ND 4.0arXiv
The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations
Abstract
We construct the Buchholz algebra without a Fock representation, as the bounded inverse limit of intrinsic particle-cutoff quotients of the gauge-fixed resolvent algebra, with isometric particle-degree coordinates. Its finite matrix corners carry canonical traces, KMS states, and trace-norm product formulas, together with closed-path expansions that lay the groundwork for path-integral representations. The known Fock-space description and a proper quasilocal subalgebra arise as realizations.
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BibTeX
@misc{sekine2026buchholz,
title = {{The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations}},
author = {Yoshitsugu Sekine},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01622},
eprint = {2610.01622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01622},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations
AU - Yoshitsugu Sekine
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01622
UR - https://arxiv.org/abs/2610.01622
AB - We construct the Buchholz algebra without a Fock representation, as the bounded inverse limit of intrinsic particle-cutoff quotients of the gauge-fixed resolvent algebra, with isometric particle-degree coordinates. Its finite matrix corners carry canonical traces, KMS states, and trace-norm product formulas, together with closed-path expansions that lay the groundwork for path-integral representations. The known Fock-space description and a proper quasilocal subalgebra arise as realizations.
ER -