论文标题
狄拉克操作员的全球和微世方面：繁殖者和哈达马州
Global and microlocal aspects of Dirac operators: propagators and Hadamard states
论文作者
论文摘要
我们提出了一种几何方法，以在cauchy-compact全球双曲线4个manifolds上为Lorentzian Dirac操作员构建Cauchy Evolution Operator。我们将Cauchy Evolution Operator视为两个不变定义的振荡积分的总和 - 正面和负面的狄拉克传播器 - 空间和及时的全局，具有杰出的复杂值几何相位函数。作为应用，我们将凯奇进化运营商与Feynman繁殖者联系起来，并构建了准hadamard国家的Cauchy表面协方差。
We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy-compact globally hyperbolic 4-manifolds. We realise the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals -- the positive and negative Dirac propagators -- global in space and in time, with distinguished complex-valued geometric phase functions. As applications, we relate the Cauchy evolution operators with the Feynman propagator and construct Cauchy surfaces covariances of quasifree Hadamard states.
