A distinguished vacuum state for a quantum field in a curved spacetime: formalism, features, and cosmology
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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.
KeywordsNonperturbative Effects Space-Time Symmetries Thermal Field Theory Cosmology of Theories beyond the SM
- R. Wald, Quantum field theory in curved spacetime and black hole thermodynamics, Chicago lectures in physics, University of Chicago Press, Chicago U.S.A. (1994).Google Scholar
- M. Reed and B. Simon, I: Functional Analysis, Volume 1 (Methods of Modern Mathematical Physics) (vol 1), Academic Press (1981).Google Scholar
- N. Afshordi, S. Aslanbeigi, M. Buck, F. Dowker and R. Sorkin, in preparation.Google Scholar