Quantization of Forms on the Cotangent Bundle
Quantization of Forms on the Cotangent Bundle
复制标题
余切丛上形式的量化
DOI：
10.1007/s002200050679
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发表时间：
1998
影响因子：
2.4
通讯作者：
T. Voronov
中科院分区：
文献类型：
--
作者：
T. Voronov
摘要：我们考虑以下量化结构。对于黎曼流形$M$，T⋆M上的形式空间被制成作用于M上的形式的算子的（完整）符号空间。这产生了符号的组合，这是形式的（“超”）交换乘法的变形。符号演算对于微分算子和动量多项式符号是精确的。我们计算自然拉普拉斯算子的符号。 （这里出现了一些类似 Weitzenböck 的漂亮恒等式。）建立了与 Ω (T⋆M) 自然等级相对应的迹线公式。使用这些公式，我们给出了高斯-邦内-陈省理的简单直接证明。我们结合泊松流形上形式的量化的一般问题来讨论这些结果。
Abstract:We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T⋆M is made into a space of (full) symbols of operators acting on forms on M. This gives rise to the composition of symbols, which is a deformation of the (“super”)commutative multiplication of forms. The symbol calculus is exact for differential operators and the symbols that are polynomial in momenta. We calculate the symbols of natural Laplacians. (Some nice Weitzenböck like identities appear here.) Formulae for the traces corresponding to natural gradings of Ω (T⋆M) are established. Using these formulae, we give a simple direct proof of the Gauss–Bonnet–Chern Theorem. We discuss these results in connection with a general question of the quantization of forms on a Poisson manifold.