We compute the vacuum polarization for a massless, conformally coupled scalar field on the covering space of global, four-dimensional, anti-de Sitter space-time. Since anti-de Sitter space is not globally hyperbolic, boundary conditions must be applied to the scalar field. We consider general Robin (mixed) boundary conditions for which the classical evolution of the field is well-defined and stable. The vacuum expectation value of the square of the field is not constant unless either Dirichlet or Neumann boundary conditions are applied. We also compute the thermal expectation value of the square of the field. For Dirichlet boundary conditions, both thermal and vacuum expectation values approach the same well-known limit on the space-time boundary conditions. For all other Robin boundary conditions (including Neumann boundary conditions), the vacuum and thermal expectation values have the same limit on the space-time boundary, but this limit does not equal that in the Dirichlet case.

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具有罗宾边界条件的全局反德西特时空量子场论

我们在全球四维反德西特时空覆盖空间上计算无质量共形耦合标量场的真空极化。由于反德西特空间不是全局双曲线的，因此必须对标量场应用边界条件。我们考虑一般罗宾（混合）边界条件，对于这些条件，场的经典演化是明确定义和稳定的。除非应用 Dirichlet 或 Neumann 边界条件，否则场的平方的真空期望值不是常数。我们还计算了场平方的热期望值。对于狄利克雷边界条件，热和真空期望值都接近时空边界条件的相同限制。对于所有其他 Robin 边界条件（包括 Neumann 边界条件），