In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in R. Making use of Bourgain’s method in conjunction with precise Strichartz estimates of S.Klainerman and D.Tataru, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation, inspired by I. Gallagher an...

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein–Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in t...

In this article, we have investigated quarkonium spectrum using the generalized Klein-Gordon equation. This has been done using suitable potentials and applying them in the Klein-Gordon equation mass term analytically and numerically. The simplicity of this model and the high accuracy of the achieved results, compared to other methods, for a relativistic computation of the quarkonium spectrum (...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

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.

It is proved that density plays a crucial role in the structure of quantum field theory. The Dirac and the Klein-Gordon equations are examined. The results prove that the Dirac equation is consistent with density related requirements whereas the Klein-Gordon equation fails to do that. Experimental data support these conclusions.

With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction u4 we define the Wick kernel of the interacting quantum field in four-dimensional space-time and consider its properties. In particular, the diagonal of this Wick kernel is (real) solutions of the classical nonlinear Klein-Gordon equation with the interaction u4.

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...

We develop a general theory to treat the linear stability of certain special solutions of second order in time evolutionary PDEs. We apply these results to standing waves of the following problems: the Klein-Gordon equation, for which we consider both ground states and certain excited states, the Klein-Gordon-Zakharov system and the beam equation. We also discuss possible applications to some n...

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positivefrequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequences...