Abstract:
We propose intensity interferometry with identical lepton pairs as an efficient tool for the estimation of the source size of the expanding hot zone produced in relativistic heavy ion collisions. This can act as a complementary method to two photon interferometry. The correlation function of two electrons with the same helicity has been evaluated for RHIC energies. The thermal shift of the rho meson mass has negligible effects on the HBT radii.

Abstract:
Recent experiments involving semiconducting quantum dots embedded in Aharonov-Bohm interferometry setups suggest that information concerning the phase of electron wavefunctions can be obtained from transport measurements. Here we review the basics of the theory of electron interferometry, some of the relevant experimental results, and recent theoretical developments attempting to shed light on the outstanding dilemmas.

Abstract:
Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10^15 (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.

Abstract:
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.

Abstract:
Three-pion interferometry is investigated for new information on the space-time structure of the pion source created in ultra-relativistic heavy-ion collisions. The two- and three-pion correlations are numerically computed for incoherent source functions based on the Bjorken hydrodynamical model, over a wide range of the kinematic variables. New information provided by three-pion interferometry, different from that provided by two-pion interferometry, should appear in the phases of the Fourier transform of the source function. Variables are identified that would be sensitive to the phases and suitable for observation. For a positive, chaotic source function, however, a variation of the three-pion phase is found to be difficult to extract from experiments. Effects of asymmetry of the source function are also examined.

Abstract:
The idea here is to use large relative velocities of electrons and nuclei in accelerator beams to increase the probability of fusion. The function of the electrons is to both screen the positive charge and to produce an increased parallel pinching current. The increase in reaction probability is estimated using the Darwin magnetic interaction energy approach.

Abstract:
The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal polarization of the scattered electrons. In order to evaluate these angular and polarization properties we consider two experimental setups in which the twisted electron beam collides with either a single well-localized atom or macroscopic atomic target. Detailed relativistic calculations have been performed for both setups and for the electrons with kinetic energy from 10 keV to 1000 keV. The results of these calculations indicate that the emission pattern and polarization of outgoing electrons differ significantly from the scattering of plane-wave electrons and can be very sensitive to the parameters of the incident twisted beam. In particular, it is shown that the angular- and polarization-sensitive Mott measurements may reveal valuable information about, both the transverse and longitudinal components of the linear momentum and the projection of the total angular momentum of twisted electron states. Thus, the Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.

Abstract:
A longstanding goal of Akira Tonomura was to observe Hanbury Brown--Twiss anti-correlations between electrons in a field-emission free electron beam. The experimental results were reported in his 2011 paper with Tetsuji Kodama and Nobuyuki Osakabe [Phys. Rev. A 83, 063616 (2011)]. An open issue in such a measurement is whether the observed anti-correlations arise from quantum statistics, or are simply produced by Coulomb repulsion between electrons. In this paper we describe a simple classical model of Coulomb effects to estimate their effects in electron beam interferometry experiments, and conclude that the experiment did indeed observe quantum correlations in the electron arrrival times.

Abstract:
We address the issue of relativistic stellar aberration requirements for the Space Interferometry Mission (SIM). Motivated by the importance of this issue for SIM, we have considered a problem of relative astrometric observations of two stars separated by angle $\theta$ on the sky with a single baseline interferometer. While a definitive answer on the stellar aberration issue may be obtained only in numerical simulations based on the accurate astrometric model of the instrument, one could still derive realistic conclusions by accounting for the main expected properties of SIM. In particular, we have analysied how the expected astrometric accuracy of determination of positions, parallaxes and proper motions will constrain the accuracy of the spaceraft navigation. We estimated the astrometric errors introduced by imperfect metrology (variations of the calibration term across the tile of interest), errors in the baseline length estimations, and those due to orbital motion of the spacecraft. We also estimate requirements on the data sampling rate necessary to apply on-board in order to correct for the stellar aberration. We have shown that the worst case observation scenario is realized for the motion of the spacecraft in the direction perpendicular to the tile. This case of motion will provide the most stringent requirement on the accuracy of knowledge of the velocity's magnitude. We discuss the implication of the results obtained for the future mission analysis.

Abstract:
We present simple and accurate analytical formulae for the rates of Compton scattering by relativistic electrons integrated over the energy distribution of blackbody seed photons. Both anisotropic scattering, in which blackbody photons arriving from one direction are scattered by an anisotropic electron distribution into another direction, and scattering of isotropic seed photons are considered. Compton scattering by relativistic electrons off blackbody photons from either stars or CMB takes place, in particular, in microquasars, colliding-wind binaries, supernova remnants, interstellar medium, and the vicinity of the Sun.