299 research outputs found
A Unique Continuation Result for Klein-Gordon Bisolutions on a 2-dimensional Cylinder
We prove a novel unique continuation result for weak bisolutions to the
massive Klein-Gordon equation on a 2-dimensional cylinder M. Namely, if such a
bisolution vanishes in a neighbourhood of a `sufficiently large' portion of a
2-dimensional surface lying parallel to the diagonal in the product manifold of
M with itself, then it is (globally) translationally invariant. The proof makes
use of methods drawn from Beurling's theory of interpolation. An application of
our result to quantum field theory on 2-dimensional cylinder spacetimes will
appear elsewhere.Comment: LaTeX2e, 9 page
An absolute quantum energy inequality for the Dirac field in curved spacetime
Quantum Weak Energy Inequalities (QWEIs) are results which limit the extent
to which the smeared renormalised energy density of a quantum field can be
negative. On globally hyperbolic spacetimes the massive quantum Dirac field is
known to obey a QWEI in terms of a reference state chosen arbitrarily from the
class of Hadamard states; however, there exist spacetimes of interest on which
state-dependent bounds cannot be evaluated. In this paper we prove the first
QWEI for the massive quantum Dirac field on four dimensional globally
hyperbolic spacetime in which the bound depends only on the local geometry;
such a QWEI is known as an absolute QWEI
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