Out-of-equilibrium electromagnetic radiation

We derive general formulas for photon and dilepton production rates from an arbitrary non-equilibrated medium from first principles in quantum field theory. At lowest order in the electromagnetic coupling constant, these relate the rates to the unequal-time in-medium photon polarization tensor and generalize the corresponding expressions for a system in thermodynamic equilibrium. We formulate the question of electromagnetic radiation in real time as an initial value problem and consistently describe the virtual electromagnetic dressing of the initial state. In the limit of slowly evolving systems, we recover known expressions for the emission rates and work out the first correction to the static formulas in a systematic gradient expansion. Finally, we discuss the possible application of recently developed techniques in non-equilibrium quantum field theory to the problem of electromagnetic radiation. We argue, in particular, that the two-particle-irreducible (2PI) effective action formalism provides a powerful resummation scheme for the description of multiple scattering effects, such as the Landau-Pomeranchuk-Migdal suppression recently discussed in the context of equilibrium QCD.Comment: 34 pages, 9 figures, uses JHEP3.cl

Bisection-based triangulations of nested hypercubic meshes

Summary. Hierarchical spatial decompositions play a fundamental role in many disparate areas of scientific and mathematical computing since they enable adaptive sampling of large problem domains. Although the use of quadtrees, octrees, and their higher dimensional analogues is ubiquitous, these structures generate meshes with cracks, which can lead to discontinuities in functions defined on their domain. In this paper, we propose a dimension–independent triangulation algorithm based on regular simplex bisection to locally decompose adaptive hypercubic meshes into high quality simplicial complexes with guaranteed geometric and adaptivity constraints.