Related papers: Non-locality and time-dependent boundary condition…
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to…
We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that…
We study the relativistic quantum motion of a spineless particle using the Feshbach-Villars (FV) formalism in the spinning cosmic string spacetime. The movement equations are derived using the first-order FV formulation of the Klein-Gordon…
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the…
We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to…
We investigate the analogue effect of the Aharonov-Bohm effect for bound states in two relativistic quantum systems in a spacetime with a space-like dislocation. We assume that the topological defect has an internal magnetic flux. Then, we…
The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
Several approaches to quantum gravity suggest that Lorentz invariance will be broken at high energy. This can lead to modified dispersion relations for wave propagation, which can be concretely realized in effective field theories where the…
Solutions to the Schr\"{o}dinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the…
In a recent paper O. Gannot and M. Wrochna considered the Klein-Gordon equation on an asymptotically anti-de Sitter spacetime subject to Robin boundary conditions, proving in particular a propagation of singularity theorem. In this work we…
We consider the problem of essential self-adjointness of the spatial part of the Klein-Gordon operator in stationary spacetimes. This operator is shown to be a Laplace-Beltrami type operator plus a potential. In globally hyperbolic…
In the framework of the relativistic generalized uncertainty principle (RGUP), we study the nonlinear Klein-Gordon field with $\phi^4$ self-interaction. This generalization comes from the quantum gravity theories that predict the existence…
There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The…
We discuss the Klein-Gordon (KG) equation using a 5D space-time approach. We explicitly show that the KG equation in flat space-time admits a consistent probabilistic interpretation with positively defined probability density. However, the…
We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $\kappa$-Poincar\'e models: for example, in the Snyder case the action of the…
In light of the significance of non-commutative quaternionic algebra in modern physics, the current study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing the…
We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove…
We study the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. Our main goal is to recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [Lindblad H.,…
We investigate the relativistic equation of state of hadronic matter and quark-gluon plasma at finite temperature and baryon density in the framework of the non-extensive statistical mechanics, characterized by power-law quantum…