论文标题
符号微几个几何IV：量化
Symplectic Microgeometry IV: Quantization
论文作者
论文摘要
我们构建了一类特殊的半经典傅立叶积分算子，其波形是符号绘画的。这些运算符具有非常好的特性：它们形成了一个类别，在该类别上，波前图成为了cotangengent Microbundle类别的函子，并且他们接受了一个总体符号积分，而符合性的微晶状形态则增强了半密度的细菌。这个新的操作员类别涵盖了半古典伪分辨率的演算，并为Schrödinger方程的半古典分析提供了功能框架。我们还对对经典和量子力学的应用以及对泊松歧管量化的功能和几何方法进行评论。
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the cotangent microbundle category, and they admit a total symbol calculus in terms of symplectic micromorphisms enhanced with half-density germs. This new operator category encompasses the semi-classical pseudo-differential calculus and offers a functorial framework for the semi-classical analysis of the Schrödinger equation. We also comment on applications to classical and quantum mechanics as well as to a functorial and geometrical approach to the quantization of Poisson manifolds.
