论文标题
C* - 代数会导致搜索量子计字段
C*-algebraic results in the search for quantum gauge fields
论文作者
论文摘要
该论文由两个部分组成，均位于操作者理论中，并且都是出于对严格量化理论的严格量化的动机。第一部分基于[Skripka，VN -JST 2022]，[van Suijlekom，VN -JNCG 2021]和[van Suijlekom，VN -JHEP 2022]，涉及非交流几何形状及其扰动扩张的光谱作用。我们证明了在相对Schatten类假设下的高阶光谱函数的存在，以Chern-simons和Yang-Mills形式进行了光谱作用的融合序列扩展，并在普遍的意义上显示了光谱作用的一环恢复性。第二部分基于[Stienstra，VN 2020]和[VN -LMP 2022]，并通过哈密顿晶格仪表理论和严格的量化涉及一种非扰动方法来实现量子规理论。我们在晶格上构建了u（1）^n-gauge的c* - 代数，表明它们是在相关时间演变下保守的，构造连续元素限制c*-代数，并表明结果构成严格的变形量化。
This thesis consists of two parts, both situated in operator theory, and both motivated by the quest for rigorous quantizations of gauge theories. The first part is based on [Skripka,vN - JST 2022], [van Suijlekom,vN - JNCG 2021], and [van Suijlekom,vN - JHEP 2022], and concerns the spectral action of noncommutative geometry and its perturbative expansions. We prove the existence of a higher-order spectral shift function under the relative Schatten class assumption, give a converging series expansion of the spectral action in terms of Chern--Simons and Yang--Mills forms, and show one-loop renormalizability of the spectral action in a generalized sense. The second part is based on [Stienstra,vN 2020] and [vN - LMP 2022] and concerns a non-perturbative approach to quantum gauge theory by means of Hamiltonian lattice gauge theory and strict quantization. We construct C*-algebras of U(1)^n-gauge observables on the lattice, show that they are conserved under the relevant time evolutions, construct continuum limit C*-algebras, and show that the result constitutes a strict deformation quantization.
