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Register a new userWigner-Moyal description of free variable mass Klein-Gordon fields
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A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in nonlinear dispersive media, thus allowing for the description of broadband radiation-matter interactions and the associated instabilities. The standard results for the classical wave action are recovered in the short wavelength limit of the generalized Wigner-Moyal formalism for the wave equation.
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We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given.
The Klein-Gordon equation is solved approximately for the Hulth{e}n potential for any angular momentum quantum number $ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a Schr{o}dinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get an energy eigenvalue and and the wave functions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We analyse this equation using the concept of analytical continuation of dispersion diagram. Particularly, it is shown that the dispersion diagram is topologically equivalent to a tube analytically embedded in two-dimensional complex space. The corresponding Fourier integral is studied on this tube using the Cauchys theorem. The basic properties of the scalar Klein-Gordon equation are established.
We study the ladder operator on scalar fields, mapping a solution of the Klein-Gordon equation onto another solution with a different mass, when the operator is at most first order in derivatives. Imposing the commutation relation between the dAlembertian, we obtain the general condition for the ladder operator, which contains a non-trivial case which was not discussed in the previous work [V. Cardoso, T. Houri and M. Kimura, Phys.Rev.D 96, 024044 (2017), arXiv:1706.07339]. We also discuss the relation with supersymmetric quantum mechanics.
Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of the nonlinear Klein-Gordon-Maxwell system and nonlinear Schroedinger-Maxwell system with subcritical nonlinearity. We prove that the number of one peak solutions depends on the topological properties of the manifold M, by means of the Lusternik Schnirelmann category.
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