论文标题
在非本地边界条件下，洛伦兹狄拉克操作员的库奇问题
The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions
论文作者
论文摘要
对于Riemannian歧管上的Dirac操作员，非本地边界条件，例如Atiyah-Patodi-Singer（APS）条件，而在具有及时边界的空位上，此类操作员以这种操作员而闻名。我们定义了一类Lorentzian边界条件，这些条件在时间上是局部的，在空间方向上是非本地的，并表明它们导致了Dirac Operator的库奇问题良好。这特别适用于在给定的cauchy时间函数的每个级别集中施加的APS条件。
Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well understood while not much is known for such operators on spacetimes with timelike boundary. We define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial directions and show that they lead to a well-posed Cauchy problem for the Dirac operator. This applies in particular to the APS conditions imposed on each level set of a given Cauchy temporal function.
