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.
Highlights
In the canonical quantization approach to quantum field theory (QFT), states of the quantum field containing particles are built up from the vacuum state using particle creation operators
The question arises as to whether modes with positive Klein–Gordon norm on CadSn can have negative frequency as seen by an observer rotating about the polar axis with angular velocity Ω
In this paper we have studied a quantum scalar field on global CadSn as seen by an observer rotating about the polar axis with angular velocity Ω
Summary
In the canonical quantization approach to quantum field theory (QFT), states of the quantum field containing particles are built up from the vacuum state using particle creation operators. On a curved space–time, in general there is no unique definition of vacuum state, there may be one or more natural, physically motivated, choices of vacuum This can be understood by considering the expansion of a free quantum field as a complete orthonormal set of field modes. Since the vacuum state is defined as the state annihilated by all the annihilation operators, its definition depends on the split into positive and negative frequency field modes. Simple toy model of Minkowski space as seen by an observer rotating about the polar axis. In this case the rotating vacuum is identical to the Minkowski vacuum [1]. If the angular velocity of the rotating observer is sufficiently small and n ≥ 4, this global vacuum contains only positive frequency particles as seen by the rotating observer
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