dc.description.abstract |
We report a non-trivial feature of the vacuum
structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say R and L separated by another region, C.
We are interested in the field theory in R ∪ L to understand
the long range quantum correlations between R and L. There
are local modes of the Dirac field having supports individually either in R or L, as well as global modes found via
analytically continuing the R modes to L and vice versa.
However, we show that unlike the case of a scalar field,
the analytic continuation does not preserve the orthogonality of the resulting global modes. Accordingly, we need to
orthonormalise them following the Gram–Schmidt prescription, prior to the field quantisation in order to preserve the
canonical anti-commutation relations. We observe that this
prescription naturally incorporates a spacetime independent
continuous parameter, θRL, into the picture. Thus interestingly, we obtain a naturally emerging one-parameter family
of α-like de Sitter vacua. The values of θRL yielding the usual
thermal spectra of massless created particles are pointed out.
Next, using these vacua, we investigate both entanglement
and Rényi entropies of either of the regions and demonstrate
their dependence on θRL. |
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