GEANT4 Simulations of Gamma-Ray Emission from Accelerated Particles in Solar Flares

Gamma-ray spectroscopy provides diagnostics of particle acceleration in solar flares, but care must be taken when interpreting the spectra due to effects of the angular distribution of the accelerated particles (such as relativistic beaming) and Compton reprocessing of the radiation in the solar atmosphere. In this paper, we use the GEANT4 Monte Carlo package to simulate the interactions of accelerated electrons and protons and study these effects on the gamma-rays resulting from electron bremsstrahlung and pion decay. We consider the ratio of the 511~keV annihilation-line flux to the continuum at 200~keV and in the energy band just above the nuclear de-excitation lines (8--15~MeV) as a diagnostic of the accelerated particles and a point of comparison with data from the X17 flare of 2003 October 28. We also find that pion secondaries from accelerated protons produce a positron annihilation line component at a depth of $\sim$ 10 g cm$^{-2}$, and that the subsequent Compton scattering of the 511~keV photons produces a continuum that can mimic the spectrum expected from the 3$\gamma$ decay of orthopositronium

Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant Symmetry in QED''

We show that recently found symmetries in QED are just non-local versions of standard BRST symmetry.Comment: 4 pages, revte

The transverse index theorem for proper cocompact actions of Lie groupoids

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.Comment: 29 page

The index of geometric operators on Lie groupoids

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid analogues of the familiar geometric operators on manifolds such as the signature and Dirac operator expressed in terms of the usual characteristic classes in Lie algebroid cohomology.Comment: 15 page

Quantization of Whitney functions

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization of Whitney functions over a closed subset of a symplectic manifold. Under the assumption that the underlying symplectic manifold is analytic and the singular subset subanalytic, we determine that the Hochschild and cyclic homology of the deformed algebra of Whitney functions over the subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page