45 research outputs found
A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
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 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
Electrostatics in a simple wormhole revisited
The electrostatic potential generated by a point charge at rest in a simple
static, spherically symmetric wormhole is given in the form of series of
multipoles and in closed form. The general potential which is physically
acceptable depends on a parameter due to the fact that the monopole solution is
arbitrary. When the wormhole has Z2-symmetry, the potential is completely
determined. The calculation of the electrostatic self-energy and of the
self-force is performed in all cases considered.Comment: 16 pages, no figure
New revival phenomena for linear integro–differential equations
We present and analyse a novel manifestation of the revival phenomenon for
linear spatially periodic evolution equations, in the concrete case of three
nonlocal equations that arise in water wave theory and are defined by
convolution kernels. Revival in these cases is manifested in the form of
dispersively quantised cusped solutions at rational times. We give an analytic
description of this phenomenon, and present illustrative numerical simulations