相关论文: Superluminal solutions to the Klein-Gordon equatio…

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the…

This dissertation discusses solutions to the nonlinear Klein-Gordon equation with symmetric and asymmetric double-well potentials, focusing on the collapse and collision of bubbles and critical phenomena found therein. A new method is…

We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…

The nature of superluminal photon propagation in the gravitational field describing radiation from a time-dependent, isolated source (the Bondi-Sachs metric) is considered in an effective theory which includes interactions which violate the…

Exact solutions of the Klein-Gordon equation in an external non-Abelian gauge field with an SU(N) symmetry group have been obtained. The external field is a solution of the Yang-Mills equations and describes a plane wave on the light cone.…

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…

We solve the Klein-Gordon equation for a massive, non-minimally coupled scalar field, with a conformal coupling, undergoing cosmological evolution from a radiation-dominated phase to a future sudden singularity. We show that, after…

The spontaneous breaking of local Lorentz invariance in the early Universe, associated with a first order phase transition at a critical time $t_c$, generates a large increase in the speed of light and a superluminary communication of…

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions…

The group-velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be Superluminal (v_g > c). By contrast, it is known that the precursor speed in vacuum…

In this paper, we prove the existence of global in time small data solutions of semilinear Klein-Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.

We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary…

The nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity, is considered. In particular, a higher-order normalized approximation of NLKG (which corresponds…

Whenever we consider any relativistic quantum wave equation we are confronted with the Klein paradox, which asserts that incident particles will suffer a surplus of reflection when dispersed by a discontinuous potential. Following recent…

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…

This is a survey of the author's recent work rather than a broad survey of the literature. The survey is concerned with the global in time solutions of the Cauchy problem for matter waves propagating in the curved spacetimes, which can be,…

In this research contribution, we explore the relativistic quantum dynamics of spin-0 scalar particles within a curved space-time background containing topological defects, while incorporating the effects of rainbow gravity. The Klein…

Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this paper, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact…

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in…

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…