标题： 量子场论对威尔逊面的表示：I 高阶共伴轨道理论 显示英文标题

标题： Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory

摘要： 这是系列论文中的第一篇，致力于严格高规范理论中威尔逊面的划分函数实现。 基于导出几何框架，提出了一种基尔洛夫-科桑特-苏里亚u理论的高版本，该框架在4维高陈-西蒙斯理论中已显示出其有用性。 提出了一种原始的导出共伴随轨道概念。 构建了导出单位线丛和正则导出轨道上的泊松结构理论。 然后确定了玻尔-索末菲量子化条件的适当导出对应物。 提出了一种导出预量子化的版本。 指出了阻碍完全量子化的问题，这些问题与其他高量子化方法共享，并提出了可能的解决办法。 我们详述的理论为配套论文中的场论构造提供了几何基础。 显示英文摘要

摘要： This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on the derived geometric framework, which has shown its usefulness in 4--dimensional higher Chern--Simons theory. An original notion of derived coadjoint orbit is put forward. A theory of derived unitary line bundles and Poisson structures on regular derived orbits is constructed. The proper derived counterpart of the Bohr--Sommerfeld quantization condition is then identified. A version of derived prequantization is proposed. The difficulties hindering a full quantization, shared with other approaches to higher quantization, are pinpointed and a possible way--out is suggested. The theory we elaborate provide the geometric underpinning for the field theoretic constructions of the companion paper.