We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing standard partial derivatives Dunkl Klein--Gordon (KG) equation. show that generalization with derivative of $z$-component angular momentum is what allows separation variables DKG Then, we compute energy spectrum and eigenfunctions equations for Coulomb potential oscillator analytically from an ${\rm su}(1,1)$ algebraic point...

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...

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.

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...

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 Green function for Klein-Gordon-Dirac equation is obtained. The case with the dominating Klein-Gordon term is considered. There seems to be a formal analogy between our problem and a certain problem for a 4-dimensional particle moving in the external field. The explicit relations between the wave function, Green function and initial conditions are established with the help of the T -exponen...

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 ...

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...

We construct small amplitude breathers in 1D and 2D Klein–Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schrödinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schrödinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum...