339 research outputs found
Quantum energy inequalities and local covariance II: Categorical formulation
We formulate Quantum Energy Inequalities (QEIs) in the framework of locally
covariant quantum field theory developed by Brunetti, Fredenhagen and Verch,
which is based on notions taken from category theory. This leads to a new
viewpoint on the QEIs, and also to the identification of a new structural
property of locally covariant quantum field theory, which we call Local
Physical Equivalence. Covariant formulations of the numerical range and
spectrum of locally covariant fields are given and investigated, and a new
algebra of fields is identified, in which fields are treated independently of
their realisation on particular spacetimes and manifestly covariant versions of
the functional calculus may be formulated.Comment: 27 pages, LaTeX. Further discussion added. Version to appear in
General Relativity and Gravitatio
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
A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime
Fewster and Mistry have given an explicit, non-optimal quantum weak energy
inequality that constrains the smeared energy density of Dirac fields in
Minkowski spacetime. Here, their argument is adapted to the case of flat,
two-dimensional spacetime. The non-optimal bound thereby obtained has the same
order of magnitude, in the limit of zero mass, as the optimal bound of Vollick.
In contrast with Vollick's bound, the bound presented here holds for all
(non-negative) values of the field mass.Comment: Version published in Classical and Quantum Gravity. 7 pages, 1 figur
Averaged Energy Inequalities for the Non-Minimally Coupled Classical Scalar Field
The stress energy tensor for the classical non-minimally coupled scalar field
is known not to satisfy the point-wise energy conditions of general relativity.
In this paper we show, however, that local averages of the classical stress
energy tensor satisfy certain inequalities. We give bounds for averages along
causal geodesics and show, e.g., that in Ricci-flat background spacetimes, ANEC
and AWEC are satisfied. Furthermore we use our result to show that in the
classical situation we have an analogue to the phenomenon of quantum interest.
These results lay the foundations for analogous energy inequalities for the
quantised non-minimally coupled fields, which will be discussed elsewhere.Comment: 8 pages, RevTeX4. Minor typos corrected; version to appear in Phys
Rev
Quantum Inequalities for the Electromagnetic Field
A quantum inequality for the quantized electromagnetic field is developed for
observers in static curved spacetimes. The quantum inequality derived is a
generalized expression given by a mode function expansion of the four-vector
potential, and the sampling function used to weight the energy integrals is
left arbitrary up to the constraints that it be a positive, continuous function
of unit area and that it decays at infinity. Examples of the quantum inequality
are developed for Minkowski spacetime, Rindler spacetime and the Einstein
closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl
Crystal truncation rods in kinematical and dynamical x-ray diffraction theories
Crystal truncation rods calculated in the kinematical approximation are shown
to quantitatively agree with the sum of the diffracted waves obtained in the
two-beam dynamical calculations for different reflections along the rod. The
choice and the number of these reflections are specified. The agreement extends
down to at least of the peak intensity. For lower intensities,
the accuracy of dynamical calculations is limited by truncation of the electron
density at a mathematically planar surface, arising from the Fourier series
expansion of the crystal polarizability
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