Related papers: Semi-classical Dirac vacuum polarisation in a scal…
We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the…
We study, through zeta-function techniques, the vacuum energies for Dirac fields in a constant magnetic background. We consider the combined effect of the background and twisted boundary conditions. The required charge renormalization is…
In the present paper, we study the semi-classical approximation of a Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear self-coupling. We prove that for a constrained coupling constant there exists a family of…
We formulate fermionic versions, for any number of spatial dimensions, of the van der Waals and Casimir-Polder interactions, and study their properties. In both cases, the systems we introduce contain localized `atoms': two-level systems,…
We analyze the gravity-induced effects associated with a massless scalar field in a higher-dimensional spacetime being the tensor product of $(d-n)$-dimensional Minkowski space and $n$-dimensional spherically/cylindrically-symmetric space…
In standard quantum electrodynamics (QED), the so-called non-minimal (Pauli) coupling is suppressed for elementary particles and has no physical implications. Here, we show that the Pauli term naturally appears in a known family of Dirac…
In the present note new effects concerned the dynamics of a charged spin-1/2 particle in a strong monochromatic plane wave background are discussed beyond the conventional dipole approximation. Namely using the semiclassical approach in the…
The Dirac structure of confinement is shown to be of timelike-vector nature in the heavy quark limit of QCD. This stands in contradiction with the phenomenological success of the Dirac scalar confining potential. A resolution is achieved…
We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials $V$ decaying like $\langle x \rangle ^{-\d}$ at infinity for some $\d >0$. By…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum…
We introduce non-minimal coupling to three-vector potential in the 3+1 dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic…
We formulate the Dirac oscillator covariantly in the presence of external non-Abelian gauge fields. More precisely, the matter field is written as $\Psi_{\alpha A}(x)$, where $\alpha$ denotes the Dirac index and $A$ the isospin index, so…
A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron-electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the…
Dirac materials have been a unique solid state platform for exploring relativistic quantum phenomena including supercritical atomic collapse, which leads to emergent discrete scale symmetry and logperiodic quantum oscillations. In the…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
We consider the Pleba{\'n}ski class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
Inthispaper,weinvestigatethescatteringtheoryofhalf-spinwavesthroughtheuse of radiation fields. We define the radiation fields for semilinear Dirac equations with spinor null forms and establish a nonlinear isomorphism between the weighted…
The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of…