We show asymptotic completeness for the charged Klein–Gordon equation in exterior De Sitter–Reissner–Nordström spacetime when product of charge black with Klein-Gordon field is small enough. then interpret scattering as transports along principal null geodesics a Kaluza–Klein extension original spacetime.

in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.

We study the scattering theory for charged Klein-Gordon equations:  (∂t − iv(x))2φ(t, x) + (x,Dx)φ(t, x) = 0, φ(0, x) = f0, i−1∂tφ(0, x) = f1, where: (x,Dx) = − ∑ 1≤j,k≤n ( ∂xj − ibj(x) ) a(x) (∂xk − ibk(x)) +m (x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential v(x) and magnetic potential ~b(x). The flow of the Kle...

Laplace operators on metric graphs give rise to Klein-Gordon and wave operators. Solutions of the Klein-Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then constructed, whose commutator function is just the Klein-Gordon kernel. As a consequence of finite propagation speed Einstein causality (local commutativity) ho...

It is proved that no Hamiltonian exists for the real Klein-Gordon field used in the Yukawa interaction. It is also shown that a real Klein-Gordon particle can be neither in a free isolated state nor in a bound state having an angular momentum l > 0. The experimental data support these conclusions. This outcome is in a complete agreement with Dirac's negative opinion on the Klein-Gordon equation.

In this paper we consider the Klein—Gordon—Maxwell system in electrostatic case, assuming fall-off large-distance requirement on gauge potential. We are interested proving existence of finite energy (and charge) standing waves, having phase corresponding to mass coefficient Klein—Gordon Lagrangian.

For free Klein-Gordon fields, we construct a one-parameter family of conserved current densities J a , with a ∈ (−1, 1), and use the latter to yield a manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. Employing a recently developed method of constructing the Hilbert space and observa...