AI 中文总结
本文无 Fock 表示构造 Buchholz 代数，通过粒子截断商的有界逆向极限实现，给出迹、KMS 态与闭路展开，为路径积分奠定基础。
AI 中文摘要
我们在没有 Fock 表示的情况下构造了 Buchholz 代数，作为规范固定预解代数的内禀粒子截断商的有界逆向极限，并带有等距粒子度坐标。其有限矩阵角携带典范迹、KMS 态和迹范数乘积公式，以及为路径积分表示奠定基础的闭路展开。已知的 Fock 空间描述和一个适当的拟局域子代数作为实现出现。
英文摘要
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.
Comments95 pages in total, including a 50-page appendix
