论文标题
具有边界和可能不均匀培养基的非紧密歧管的经典和量子光子场
The classical and quantum photon field for non-compact manifolds with boundary and in possibly inhomogeneous media
论文作者
论文摘要
在本文中，我在具有边界和可能不均匀培养基的非紧凑型歧管上对经典和量子光子场进行了严格的结构。这种结构因零模型的存在而变得复杂，这些模型可能在歧管或边界的非平凡拓扑结构中出现。一个重要的特殊情况是$ \ mathbb {r}^3 $带有障碍。在这种情况下，零模式就障碍的拓扑而有直接的解释。我根据具有相对边界条件的差分形式的频谱计算来给出了重构应力能量张量的公式。
In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary and in possibly inhomogeneous media. Such a construction is complicated by the presence of zero-modes that may appear in the presence of non-trivial topology of the manifold or the boundary. An important special case is $\mathbb{R}^3$ with obstacles. In this case the zero modes have a direct interpretation in terms of the topology of the obstacle. I give a formula for the renormalised stress energy tensor in terms of an integral kernel of an operator defined by spectral calculus of the Laplace Beltrami operator on differential forms with relative boundary conditions.
