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Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
The issue of de Sitter invariance for a massless minimally coupled scalar
field is revisited. Formally, it is possible to construct a de Sitter invariant
state for this case provided that the zero mode of the field is quantized
properly. Here we take the point of view that this state is physically
acceptable, in the sense that physical observables can be computed and have a
reasonable interpretation. In particular, we use this vacuum to derive a new
result: that the squared difference between the field at two points along a
geodesic observer's space-time path grows linearly with the observer's proper
time for a quantum state that does not break de Sitter invariance. Also, we use
the Hadamard formalism to compute the renormalized expectation value of the
energy momentum tensor, both in the O(4) invariant states introduced by Allen
and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum
energy density in the O(4) invariant case is larger than in the de Sitter
invariant case.Comment: TUTP-92-1, to appear in Phys. Rev.