We study reparametrization-invariant systems, mainly the relativistic particle and its D-dimensional extended object generalization d-brane. The corresponding matter Lagrangians naturally contain background interactions, like electromagnetism and gravity. For a dbrane that doesn’t alter the background fields, we define non-relativistic equations assuming integral sub-manifold embedding of the d...

We brieey review the current status of the algebraic approach to quantum eld theory on globally hyperbolic spacetimes, both axiomatic { for general eld theories, and constructive { for a linear Klein-Gordon model. We recall the concept of F-locality, introduced in the latter context in BS Kay: Rev. and explain how it can be formulated at an axiomatic level for a general eld theory (as a conditi...

In this paper the quantum hyperbolic equation formulated in [1] is applied to the study of the propagation of the initial thermal state of the Universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced, VP = h̄/8tP = 1.25 10 GeV where tP is a Planck time. For the barrier height V < VP the master thermal equation is the modified Klein-Gordon ...

We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a timedependent inner product. We apply our general results t...

The energy spectrum of Klein-Gordon particles is obtained via the non-minimal coupling of Klein-Gordon fields to Cartan torsion in the approximation of Riemann-flatness and constant torsion.When the mass squared is proportional to torsion coupling constant it is shown that the splitting of energy does not occur.I consider that only the vector part of torsion does not vanish and that it is const...

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coup...

We analyze the Kaluza–Klein type procedure in AdS3 space called dimensional degression. The topological theory of Fronsdal field is reformulated terms fields propagating AdS2. find that leads to finitely many modes. Namely, obtained spectrum massive Klein–Gordon and Proca result derived by using specific mode expansion, gauge fixing, 2–dimensional Schouten identities.

We deal with the derivation of the Schrödinger-Poisson system as a non-relativistic limit (i.e. c→∞ where c is the speed of light) of the Klein-GordonMaxwell or the Dirac-Maxwell system on R. We deal with convergence in the energy space C([0, T ];H). We use and motivate a splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to elect...

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein–Gordon equation can be used as numerical algorit...

The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that, in an appropriate probability space, the difference between the average of all solutions that satisfy certain constraints at time t = 0 and the average computed by an approximate method is small with high probability.