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