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Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to first post-Minkowskian order. The potential develops an instability in the strong field regime which is expected from an…
Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only…
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the…
We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O'Raifeartaigh et al. in…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is…
We consider an interacting system of spinor and electromagnetic field, explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the…
Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and…
We embed the component fields of eleven-dimensional supergravity into a superspace of the form $X\times Y$ where $X$ is the standard 4D, $N=1$ superspace and $Y$ is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
In this work we consider a scale-tensor theory in which the space-time is endowed with a Weyl integrable geometrical structure due to the Palatini variational method. Since the scalar field has a geometrical nature (related to…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled…
In this work, a new integral equation (IE) based formulation is proposed using vector and scalar potentials for electromagnetic scattering. The new integral equations feature decoupled vector and scalar potentials that satisfy Lorentz…
In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…