Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot take place. By contrast, the Dirac equation is free of these problems. Other inconsistencies arise if the KleinGordon field is regarded as a classical field.

Abstract. We present some recent trends in the theory of Klein-Gordon-Schrödinger type Systems. Then we give some resent results on the following special type of a dissipative Klein-Gordon-Schrödinger System iψt + κψxx + iαψ = φψ, x ∈ Ω, t > 0, φtt − φxx + φ+ λφt = −Reψx, x ∈ Ω, t > 0, satisfying the initial and boundary conditions ψ(x, 0) = ψ0(x), φ(x, 0) = φ0(x), φt(x, 0) = φ1(x), x ∈ Ω, ψ(x,...

We introduce and discuss the generalized Klein-Gordon second-order partial differential equation in the Robertson-Walker space-time, using the Casimir second-order invariant operator written in hyperspherical coordinates. The de Sitter and anti-de Sitter space-times are recovered by means of a convenient choice of the parameter associated to the space-time curvature. As an application, we discu...

Herein, the Dirac equation is compared with the KleinGordon equation. In contrast to the Dirac case, it is proved that the Klein-Gordon equation has difficulties with the Hamiltonian differential operator of relativistic quantum mechanics and with the definition of an inner product of wave functions, which is a requirement for a construction of a Hilbert space. An added discussion of the Pauli-...

In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a functio...

We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example, we get solutions that mimic the Harmonic oscillator energy levels, surprisingly. An equation similar to the beam equation is obtained in the process.

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential V (r) is established. It is shown that Nmπ = π (nm − n−m) = [δm(M) + β1]− [δm(−M) + β2] ,where Nm denotes the difference between the number of bound states of the particle nm and the ones of antiparticle n−m with a fixed angular momentum m, and the δm is named phase shifts. The constants ...

In this paper, we study the existence and uniqueness of global solution for a Klein–Gordon equations system with mixed boundary conditions. We, also, analyze asymptotic behavior solution.

Abstract All causal Lie products of solutions the Klein-Gordon equation and wave in Minkowski space are determined. The results shed light on origin algebraic structures underlying quantum field theory.

Klein–Gordon equation with pseudoharmonic oscillator has been corrected through physical acceptable solutions. In a way, we correct the energy spectra related to its behavior versus potential parameter D e .