Higher U(1)-gerbe connections in geometric prequantization
Higher U(1)-gerbe connections in geometric prequantization
复制标题
几何预量化中更高的 U(1)-gerbe 连接
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
U. Schreiber
中科院分区：
文献类型：
--
作者：
D. Fiorenza;Christopher L. Rogers;U. Schreiber
我们将几何预量化提升到更高的几何形状（更高的堆栈），其中预量化由更高的主连接（具有连接的更高的 gerbe）给出。我们相当普遍地展示了如何存在规范地分配给更高预量化的更高规范群群和库朗群群的塔，并建立相应的 Atiyah 序列作为通过更高量子同态的更高哈密顿辛同态的集成 Kostant-Souriau ∞ 群扩展。我们还展示了对这种扩展进行分类的 ∞ 群余循环，并讨论了它对哈密顿 ∞ 作用的限制如何产生更高的海森堡余循环。在光滑流形上的更高阶微分几何的特殊情况下，我们发现了哈密顿向量场的 L∞ 代数扩展——这是局部可观测量的更高泊松括号——并表明它等价于第二作者在 n 重几何中提出的构造。最后，我们列出了在局域量子场论的扩展几何量化中，特别是在弦几何中应用更高预量化的示例列表。
We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant–Souriau ∞-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the ∞-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian ∞-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the L∞-algebra extension of Hamiltonian vector fields — which is the higher Poisson bracket of local observables — and show that it is equivalent to the construction proposed by the second author in n-plectic geometry. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.