相关论文: The Klein-Gordon equation on asymptotically Minkow…

The Schwinger-Dyson equation for a scalar propagator is solved in Minkowski space with the help of an integral spectral representation, both for spacelike and timelike momenta. The equation is re-written into a form suitable for numerical…

For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If…

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…

We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conceptually simple construction of fundamental solution…

A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the…

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…

We find three exact solutions to the Klein-Gordon equation in 1-1 dimensional space-time for different time dependent potentials. In two cases we consider a time dependent scalar potential and in one case a time dependent electric…

Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…

In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…

We give estimates for the changes of the eigenvalues of the Klein Gordon operator under the change of the potential. In some relevant situations we improve the existing estimates. We test our results on some exactly solvable models (Coulomb…

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on massive scalar fields. We obtain an exact solution of the Klein-Gordon equation in this spacetime, which…

We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…

We develop a fully gauge invariant analysis of gravitational wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model, whose constant curvature solution provides a natural deSitter background for…

We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…

We prove $\ell^{1}\!\to\!\ell^{\infty}$ dispersive estimates for the discrete Klein--Gordon equation on $\mathbb Z$ with small real-analytic quasi-periodic potentials, showing that the time-decay rate persists as $(\tfrac13)^{-}$. As…

In this paper, we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is…

In this note, we study a geometric property of asymptotically Minkowski spacetimes and an analytic property of the Klein-Gordon operator. Precisely, our first main results show that asymptotically Minkowski spacetimes are geodesically…

We analyse the complex-valued Klein-Gordon Equation from an integrability perspective by the implementation of the Lie Theory of Continuous Groups, where this equation is governed by power-law nonlinearity. We write the equations in terms…

In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity condition and a generalized weighted Kirchhoff condition for…