We consider a real massive free quantum scalar field with arbitrary curvature coupling on n-dimensional anti-de Sitter spacetime. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for n ¼ 2 to n ¼ 11 inclusive.

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We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter space-time. Anti-de Sitter space-time is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green's functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values. The thermal Feynman Green's functions are constructed from the vacuum Feynman Green's functions using the imaginary time periodicity/anti-periodicity property for scalars/fermions. Focussing on massless fields with either conformal or minimal coupling to the space-time curvature (these two cases being the same for fermions) we compute the differences between the thermal and vacuum expectation values. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.

We consider the definition of the global vacuum state of a quantum scalar field on n-dimensional anti-de Sitter space-time as seen by an observer rotating about the polar axis. Since positive (or negative) frequency scalar field modes must have positive (or negative) Klein-Gordon norm respectively, we find that the only sensible choice of positive frequency corresponds to positive frequency as seen by a static observer. This means that the global rotating vacuum is identical to the global nonrotating vacuum. For n ≥ 4, if the angular velocity of the rotating observer is smaller than the inverse of the anti-de Sitter radius of curvature, then modes with positive Klein-Gordon norm also have positive frequency as seen by the rotating observer. We comment on the implications of this result for the construction of global rotating thermal states.

We outline an analytic method for computing the renormalised vacuum expectation value of the quadratic fluctuations and stress-energy tensor associated with a quantised scalar field propagating on AdSn. Explicit results have been obtained using Hadamard renormalisation in the case of a massive neutral scalar field with arbitrary coupling to the curvature, for n = 2 to n = 11 inclusive.