16,787 research outputs found
Distributional Asymptotic Expansions of Spectral Functions and of the Associated Green Kernels
Asymptotic expansions of Green functions and spectral densities associated
with partial differential operators are widely applied in quantum field theory
and elsewhere. The mathematical properties of these expansions can be clarified
and more precisely determined by means of tools from distribution theory and
summability theory. (These are the same, insofar as recently the classic
Cesaro-Riesz theory of summability of series and integrals has been given a
distributional interpretation.) When applied to the spectral analysis of Green
functions (which are then to be expanded as series in a parameter, usually the
time), these methods show: (1) The "local" or "global" dependence of the
expansion coefficients on the background geometry, etc., is determined by the
regularity of the asymptotic expansion of the integrand at the origin (in
"frequency space"); this marks the difference between a heat kernel and a
Wightman two-point function, for instance. (2) The behavior of the integrand at
infinity determines whether the expansion of the Green function is genuinely
asymptotic in the literal, pointwise sense, or is merely valid in a
distributional (cesaro-averaged) sense; this is the difference between the heat
kernel and the Schrodinger kernel. (3) The high-frequency expansion of the
spectral density itself is local in a distributional sense (but not pointwise).
These observations make rigorous sense out of calculations in the physics
literature that are sometimes dismissed as merely formal.Comment: 34 pages, REVTeX; very minor correction
Antineutrino flux from the Laguna Verde Nuclear Power Plant
We present a calculation of the antineutrino flux produced by the reactors at
the Laguna Verde Nuclear Power Plant in M\'exico, based on the antineutrino
spectra produced in the decay chains of the fission fragments of the main
isotopes in the reactor core, and their fission rates, that have been
calculated using the DRAGON simulation code. We also present an estimate of the
number of expected events in a detector made of plastic scintillator with a
mass of 1 ton, at 100 m from the reactor cores.Comment: 15 pages, 8 figures, 4 table
Surface Vacuum Energy in Cutoff Models: Pressure Anomaly and Distributional Gravitational Limit
Vacuum-energy calculations with ideal reflecting boundaries are plagued by
boundary divergences, which presumably correspond to real (but finite) physical
effects occurring near the boundary. Our working hypothesis is that the stress
tensor for idealized boundary conditions with some finite cutoff should be a
reasonable ad hoc model for the true situation. The theory will have a sensible
renormalized limit when the cutoff is taken away; this requires making sense of
the Einstein equation with a distributional source. Calculations with the
standard ultraviolet cutoff reveal an inconsistency between energy and pressure
similar to the one that arises in noncovariant regularizations of cosmological
vacuum energy. The problem disappears, however, if the cutoff is a spatial
point separation in a "neutral" direction parallel to the boundary. Here we
demonstrate these claims in detail, first for a single flat reflecting wall
intersected by a test boundary, then more rigorously for a region of finite
cross section surrounded by four reflecting walls. We also show how the
moment-expansion theorem can be applied to the distributional limits of the
source and the solution of the Einstein equation, resulting in a mathematically
consistent differential equation where cutoff-dependent coefficients have been
identified as renormalizations of properties of the boundary. A number of
issues surrounding the interpretation of these results are aired.Comment: 22 pages, 2 figures, 1 table; PACS 03.70.+k, 04.20.Cv, 11.10.G
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