利用微分几何结构对Kostant-Souriau量子化映射的重言式调谐
Tautological Tuning of the Kostant-Souriau Quantization Map with Differential Geometric Structures
AI总结：
针对规范量子化的特设性及现有几何/形变量子化的局限，本文提出仅用辛几何与黎曼几何微分结构（如重言式1-形式）的重言式调谐量子化，更贴近规范量子化且适用于协变哈密顿场论。
摘要：
数十年来，数学物理学家一直在寻找一种坐标无关的量子化程序，以取代规范量子化的特设过程。这一努力在很大程度上合并为两个不同的研究方向：几何量子化和形变量子化。尽管这两个方向都取得了诸多成功，但由于其数学复杂性以及作为经验模型的实际失效，它们均未在更注重实验的量子物理学界获得主流认可。本文提出了一种坐标无关量子化的替代方法，称为重言式调谐量子化。该方法仅使用辛几何和黎曼几何中的微分几何结构，尤其是重言式1-形式和向量场（因此得名）。在对物理重要函数的关注上，重言式调谐量子化比传统几何量子化或形变量子化更贴近规范量子化的特设方法，从而避免了这些方法面临的一些数学挑战。鉴于其对标准微分几何结构的关注，重言式调谐量子化也是比传统几何或形变量子化更适合应用于协变哈密顿场论的候选方法，因此可能为经典场的几何量子化铺平道路。
英文摘要：
For decades, mathematical physicists have searched for a coordinate independent quantization procedure to replace the ad hoc process of canonical quantization. This effort has largely coalesced into two distinct research programs: geometric quantization and deformation quantization. Though both of these programs can claim numerous successes, neither has found mainstream acceptance within the more experimentally minded quantum physics community, owing both to their mathematical complexities and their practical failures as empirical models. This paper introduces an alternative approach to coordinate-independent quantization called tautologically tuned quantization. This approach uses only differential geometric structures from symplectic and Riemannian geometry, especially the tautological one form and vector field (hence the name). In its focus on physically important functions, tautologically tuned quantization hews much more closely to the ad hoc approach of canonical quantization than either traditional geometric quantization or deformation quantization and thereby avoid some of the mathematical challenges faced by those methods. Given its focus on standard differential geometric structures, tautologically tuned quantization is also a better candidate than either traditional geometric or deformation quantization for application to covariant Hamiltonian field theories, and therefore may pave the way for the geometric quantization of classical fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
