论文标题
在三维抗DE保姆时空时空上真空极化，可替代罗宾边界条件
Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
论文作者
论文摘要
我们研究了一个量子标量场，并具有一般质量和耦合到标量曲率，并在三维全球抗DE保姆时空上传播。我们确定了场平方的真空和热期望值，也称为真空极化（VP）。我们考虑标量场质量和耦合的值，其中有一些边界条件可以提供良好的经典动力学。我们将Dirichlet，Neumann和Robin（混合）边界条件应用于时空边界的场地。当管理罗宾边界条件的参数低于某个临界值时，我们发现VP的有限值。对于所有耦合，具有Neumann或Dirichlet边界条件的VP的真空期望值是恒定的，并且尊重背景时空的最大对称性。但是，当真空和热期望值都取决于时空位置时，罗宾边界条件并非如此。在时空边界上，我们发现，当应用诺伊曼边界条件时，具有罗宾边界条件的VP的真空和热期望值会收敛到结果，除非在Dirichlet边界条件的情况下。
We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions.
