Related papers: Hohenberg-Kohn Theorems in Electrostatic and Unifo…
Density Functional Theory's Kohn-Sham (KS) potential emerges as the minimizing effective potential in an unconstrained variational scheme that does not involve fixing the unknown single-electron density. The physical content behind the…
In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For…
We advocate the study of external-field quantum electrodynamics with $N$ charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large $N$ limit which receives contributions from all loop…
The thermodynamical analogy of density functional theory, which is an organic part of the spin-independent version of the theory, is reconsidered for its spin-polarized generalization in view of the recently uncovered nonuniqueness of the…
Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
It is known that the asymptotic decay of the electron density $n(\br)$ outside a molecule is informative about its first ionization potential $I_0$, $n(|\br|\to\infty) \sim \text{exp}(-2\sqrt{2I_0}\,r)$. This dictates the orbital energy of…
Motivated by the long-debated question about the internal stability of the electron, the force densities acting on the charge density of the 1s electron in the H atom are investigated. The problem is mapped onto the canonical formalism for…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
In gauge theories, observable quantities have to be gauge-invariant. In general, this requires composite operators, which usually have substantially different properties, e.g. masses, than the elementary particles. Theories with a Higgs…
We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is…
Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard…
Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration…
We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite…
In the accompanying Comment [Phys. Rev. A {\bf 67}, 056501 (2003)], I. Lindgren and S. Salomonson claim to prove for the Kohn-Sham kinetic energy functional of ground state electron density that a Fr\"echet functional derivative exists,…
In Einstein-scalar-Maxwell theories with a coupling between the scalar field $\phi$ and the electromagnetic field strength $F$ of the form $\mu(\phi) F$, we investigate the existence of exotic compact objects (ECOs) and their observational…
The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the ground-state energy or, at finite temperatures, to the free…
In a previous work, the meaning of the Planck constant $h = \left( e^2 / 2 \alpha \right) \sqrt{\mu_0 / \epsilon_0}$, accomplished by solving Maxwell's electrodynamics laws with specific electric $1 / \tau_C = 1 / R_q C_q$ and magnetic $1/…
Quantum spin rings represent an intriguing platform for studying unconventional magnetic order and exotic quantum phases, and they are also promising materials for emerging quantum technologies. Conventional spin systems consist of a set of…