标题： 从U(1)全纯代数的Fock表示 显示英文标题

标题： Fock representations from U(1) holonomy algebras

摘要： 我们重新考察使用基于阿贝尔C*代数的技术来对U(1)全纯代数进行量化，这些技术是当前构建环量子引力努力的数学基础。 特别是，我们澄清了“模糊环”和洛伦兹不变性在这些代数的福克表示构造中的作用。 这使我们能够通过应用当时环量子引力的（当前）技术，对早期开创性努力进行批判性重新审视，这些努力试图从全纯代数构造线性化引力和自由麦克斯韦理论的福克空间表示。 显示英文摘要

摘要： We revisit the quantization of U(1) holonomy algebras using the abelian C* algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of ``smeared loops'' and of Poincare invariance in the construction of Fock representations of these algebras. This enables us to critically re-examine early pioneering efforts to construct Fock space representations of linearised gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.