2020/04/06 by Thomas Morley, Peter J. Taylor, Morley, Thomas +3
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2004.02704
We compute the vacuum polarization for a massless, conformally coupled scalar\nfield on the covering space of global, four-dimensional, anti-de Sitter\nspace-time. Since anti-de Sitter space is not globally hyperbolic, boundary\nconditions must be applied to the scalar field. We consider general Robin\n(mixed) boundary conditions for which the classical evolution of the field is\nwell-defined and stable. The vacuum expectation value of the square of the\nfield is not constant unless either Dirichlet or Neumann boundary conditions\nare applied. We also compute the thermal expectation value of the square of the\nfield. For Dirichlet boundary conditions, both thermal and vacuum expectation\nvalues approach the same well-known limit on the space-time boundary\nconditions. For all other Robin boundary conditions (including Neumann boundary\nconditions), the vacuum and thermal expectation values have the same limit on\nthe space-time boundary, but this limit does not equal that in the Dirichlet\ncase.\n