The global rotating scalar field vacuum on anti-de Sitter space–time

Abstract

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.

Thermal expectation values of fermions on anti-de Sitter space-time

“…On adS, due to the time-like boundary, there may or may not be an SOL depending on the angular speed of rotation [18]. For a quantum scalar field, the only possible global vacuum state on adS is the nonrotating vacuum [38]. We conjecture that the situation for a quantum fermion field is likely to be different and expect to be able to define a rotating vacuum.…”

“…What about rotating states on adS? For a quantum scalar field, as on Minkowski space-time, the rotating and nonrotating vacua coincide [51], irrespective of whether or not there is an SLS surface. In this paper we examine what happens for a quantum fermion field on adS.…”

Quantum field theory on global anti-de Sitter space-time with Robin boundary conditions

“…Therefore computing the vacuum polarization at ρ = 0 will give the correct answer on the entire space-time. The asymptotics of the Legendre functions [46], 25) implies that near the origin only the ℓ = 0 mode contributes [8]. Moreover, the ℓ = 0 radial modes for the Dirichlet case are…”

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

“…What about rotating states on adS? For a quantum scalar field, as on Minkowski space-time, the rotating and nonrotating vacua coincide [51], irrespective of whether or not there is an SLS. In this paper we examine what happens for a quantum fermion field on adS.…”