Finite temperature field theory with boundaries: Stress tensor and surface action renormalisation

The local stress tensor is calculated for a scalar field at finite temperature in a static spacetime with boundaries. Results exact in the temperature are obtained which in the zero temperature limit exhibit known non-integrable divergences as the boundary is approached. Renormalisation of bare surface gravitational actions produces a delta function behaviour in the energy density on the boundary which exactly cancels the local divergences, thereby rendering finite the total renormalised energy in a cavity. The role played by boundary contributions to the integrated quantum mechanical propogator for a finite system is emphasised.