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Fundamental theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are…

A finite quantum gravity theory is used to resolve the cosmological constant problem. A fundamental quantum gravity scale, \Lambda_G \leq 10^{-3} eV, is introduced above which the quantum corrections to the vacuum energy density coupled to…

We demonstrate that classical and quantum electrodynamics can be completed by gravitational torsion appearing in Einstein-Cartan-Sciama-Kibble theory of gravity, providing the missing part of the electron theory. One of the equations of…

The work shows that the associated Einstein like gravity for the Klein-Gordon field shows the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). Even…

The self-force of classical electrodynamics on a charged "rigid" body of radius R is evaluated analytically for the body undergoing a slow (i.e., with a speed v<<c), slight (i.e., small compared to R), and temporary displacement from an…

We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum…

We explore the space of solutions of the classical equations of motion in the Euclidean electroweak theory. We sketch a topological prescription that finds known solutions and indicates the existence of novel ones. All spatially-varying,…

We give a quantum field theoretical derivation of the scalar Abraham-Lorentz-Dirac (ALD) equation and the self-force for a scalar charged particle interacting with a quantum scalar field in curved spacetime. We regularize the causal Green's…

Although the expressions for energy densities involving electric and magnetic fields are exactly analogous, the connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, the changes in the…

In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical…

The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…

We explore quantum corrections of electrically charged black holes subject to vacuum polarization effects of fermion fields in QED. Solving this problem exactly is challenging so we restrict to perturbative corrections that one can obtain…

A fully consistent classical relativistic electrodynamics with spinless point charges is constructed. The classical evolution of the electromagnetic fields is governed by the nonlinear Maxwell--Born--Infeld field equations, the classical…

We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue - even earlier. However, it seems that physics…

The electromagnetic self-force equation of motion is known to be afflicted by the so-called runaway problem. A similar problem arises in the semiclassical Einstein's field equation and plagues the self-consistent semiclassical evolution of…

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead…

The search of the correct equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field, the so-called \textit{radiation-reaction equation of motion}, remains elusive to date. In this paper we…

The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…

In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the…

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral…