Worldsheet Instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.Comment: 40 pages; Expanded discussion section, added reference

Electronic zero modes of vortices in Hall states of gapped graphene

Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall state of graphene has inspired the idea that charge carriers in the metallic state could be fractionally charged vortices. We examine the question of whether vortices in particular gapped states of graphene and subject to external magnetic and pseudo-magnetic fields could have the mid-gap zero mode electron states which would allow them to be charged.Comment: 8pg

Arc electrode of graphite with ball tip Patent

Arc electrode of graphite with tantalum ball ti

Control apparatus for spectral energy source

Automatic light-controlling system for dc arc emission spectrographs controls the vaporization rate of the sample and stabilizes the dc arc. The output energy is regulated such that advantage can be taken of the highly sensitive dc arc source without sacrificing the desired precision

Simplified procedure for emission spectrochemical analysis

Procedure involves dissolution of samples to prepare them for analysis, and uses single set of experimental conditions to analyze wide variety of materials and compositions without compromising analysis accuracy. Automated spectrometer alloys per sample analysis time of four minutes after sample dissolution

Let us pray with confidence : Leaders of the Assembly Prepare

(Excerpt) Let us pray with confidence in the words our Savior gave us, calls out the presider to the assembly. Or, perhaps, another introduction is used: As our Savior Christ has taught us, we are bold to say, for example. Or, perhaps, the presider simply begins-enacting the confidence that the introductory texts call for-the assembly easily catching on that this is a communal act and joining in: Our Father in heaven, hallowed be your name ... In any case, here is an archetypal act of presiding: the leader proposing an important, beloved and known-by-heart act of prayer and drawing the entire assembly into its practice in a known-by-heart place