The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

THE THERMAL FORM OF THE PHOTOEFFECT WITH THE DEBYE AND THE WIGNER CRYSTAL

We define the photoelectric effect with the specific heat term replacing the work function. The photon propagator involving the radiative correction is also considered. We consider the Debye specific head for the 3D crystal medium, the specific heat for the 2D medium and specific heat for the Wigner crystal.

Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to most of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded dyadic Green function, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. Using the photon propagator in a material, expressed in the relevant gauges, as a tool to understand the interaction between a fast electron and a material, we extend this relation to a newly defined quantity, the relativistic MDFF. The relation between the dyadic Green function and the relativistic MDFF does depend only on the photon propagator and not on the specifics of the particle (here, a fast electron) probing the target. Therefore, it can be adapted to any spectroscopy where a relation between the electromagnetic and electronic properties of a material is needed. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.

The Nonrelativistic Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting form the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

PHOTONS GENERATED BY PLASMA FLUCTUATIONS

The totally ionized charged collisionless plasma at finite temperature is considered. Using the statistical and Schwinger field methods we derive the production of photons from the plasma by the Cerenkov mechanism. We derive the spectral formula of emitted photons by the plasma fluctuations. The calculation can be extended to the photon propagator involving radiative corrections.

Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

We discuss an inherent Pauli–Villars regularization in Bopp–Podolsky’s generalized electrodynamics. Introducing gauge-fixing terms for Bopp–Podolsky’s generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli–Villars regularization independent of the gauge choice made in Maxwell’s usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp–Podolsky’s higher order derivatives corresponds to the inverse of the Pauli–Villars regularization mass scale $$\Lambda $$Λ, i.e. $$a = 1/\Lambda $$a=1/Λ. Solving explicitly the classical static Bopp–Podolsky’s equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.