Related papers: Non-Volkov solutions for a charge in a plane wave
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
The Klein-Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the…
Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex…
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…
We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua.…
We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like…
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present…
A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously developed and applied to Yang--Mills theory in Coulomb gauge, is generalized to full QCD. The…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic…
The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
We address the Klein-Gordon equation for a spinless charged particle in the presence of an electromagnetic (EM) field, and focus on its known shortcoming, related to the existence of solutions with a negative probability density. We…
We study gravitational plane impulsive waves and electromagnetic shock waves in a scalar-tensor theory of gravity of the Brans-Dicke type. In vacuum, we present an exact solution of Brans-Dicke's field equations and give an example in which…
The exact solutions of the Dirac equation in an external non-abelian SU(N) gauge field which is in the form of a plane wave on the light cone is obtained. The whole set of the solutions for both particles and anti-particle is constructed.