Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications.We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

The Stripe of Electron Diffraction in Magnetic Field—A Counterexample. In Electric Field, the Result Will Be the Same

As long as no one has done diffraction experiment in the spark chamber (DESC) , it makes sense to do this experiment. This experiment has two possible results: (1) Diffraction fringes cannot be obtained; (2) Path information and diffraction patterns can be obtained at the same time. If the result is (1), it provides direct and unambiguous experimental evidence for the existing Copenhagen quantum mechanics interpretation system, which can avoid some unnecessary disputes; If the result is (2), it will cause a scientific revolution in the field of quantum mechanics interpretation (After all, most people now think that "as long as the particle path is observed in the double slit experiment, the interference fringes will disappear"). "The result of the electron diffraction experiment in a magnetic field—diffraction fringes can still be obtained" was discovered. This finding provides an experimental evidence for DESC to be meaningful and predicts that the experimental result of DESC is the result (2).

Thermal and Flow Characteristics of Discrete Double Inclined Ribs at Low Curvature Coil for GSHP Application

In this study, the thermal and hydraulic characteristics in low curvature coil with Discrete Double Inclined Ribs (DDIR) were investigated. Water is selected as a working fluid, and flowrate range from 1 to 5 L/min, which is a low flowrate condition. Effect of geometry parameters such as distance between ribs, curvature ribs, and ribs inclination angles was observed. Results obtained by numerical simulations show that the heat transfer in DDIR-coil is 7.7 to 29.11% greater than that in plain coil, while the pressure drop was approximately 12.7 to 89.5% larger than that of plain-coil. A COP improvement factor that is calculated based on energy loss by pressure drop and energy saving by heat transfer enhancement was found to vary between 0.25 and 5.29. Flow visualization shows that there are two vortexes in cross-section at the downstream, and local vortexes arise around the ribs of DDIR-coil, which shows similar pattern and strength to DDIR-straight tube. The vortex makes a long fluid particle path and strengthens the turbulent mixing between the wall and the core flow of the coil. Based on these findings, DDIR-coil is recommended for applications in Slinky Ground Heat Exchangers, especially at low flowrates.

Calculation of flow in incompressible regenerative turbo-machines with bucket form blades based on the geometry of flow path

Purpose Regenerative flow pumps are dynamic machines with the ability to develop high heads at low flow rates. Simplicity, compactness, stable features and low manufacturing costs make them interesting for many applications in industries. The purpose of this study is to present a new method for calculating the flow through regenerative pumps with bucket form blades to predict the performance curves by a cheap and easy-to-use way. Design/methodology/approach The analysis was carried out based on the geometric shape of a fluid particle trajectory in a regenerative turbomachine. The fluid particle path was assumed to be a helix wrapped into a torus. Loss models were considered and the results of predictions were compared with computational fluid dynamics (CFD) data. Findings The overall trend of performance curves resulted from presented model looked consistent with CFD data. However, there were slight differences in high and low flow coefficients. The results showed that the predicted geometric shape of the flow path with the presented model (a helix wrapped into a torus) was not consistent with CFD results at high flow coefficients. Due to the complexity and turbulence of the fluid flow and errors in the calculation of losses, as well as slip factor, there was a discrepancy between the results of the presented model and numerical simulation, especially in high and low flow coefficients. Originality/value The analysis was carried out based on the geometric shape of a fluid particle trajectory in a regenerative turbomachine with bucket form blades. The fluid particle path was assumed to be a helix wrapped into a torus.