Abstract
We define a distinguished “ground state” or “vacuum” for a free scalar quantum field in a globally hyperbolic region of an arbitrarily curved spacetime. Our prescription is motivated by the recent construction [1, 2] of a quantum field theory on a background causal set using only knowledge of the retarded Green’s function. We generalize that construction to continuum spacetimes and find that it yields a distinguished vacuum or ground state for a non-interacting, massive or massless scalar field. This state is defined for all compact regions and for many noncompact ones. In a static spacetime we find that our vacuum coincides with the usual ground state. We determine it also for a radiation-filled, spatially homogeneous and isotropic cosmos, and show that the super-horizon correlations are approximately the same as those of a thermal state. Finally, we illustrate the inherent non-locality of our prescription with the example of a spacetime which sandwiches a region with curvature in-between flat initial and final regions.
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ArXiv ePrint: 1205.1296
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Afshordi, N., Aslanbeigi, S. & Sorkin, R.D. A distinguished vacuum state for a quantum field in a curved spacetime: formalism, features, and cosmology. J. High Energ. Phys. 2012, 137 (2012). https://doi.org/10.1007/JHEP08(2012)137
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DOI: https://doi.org/10.1007/JHEP08(2012)137