Symplectic groups and the Klein-Gordon field

Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field

The difference between a Klein-Gordon random field and the complex Klein-Gordon quantum field is characterized, explicitly comparing the roles played by negative frequency modes of test functions in creation and annihilation operator presentations of the two theories. The random field and the complex quantum field can both be constructed from the same creation and annihilation operator algebra,...

Symplectic Finite Diierence Approximations of the Nonlinear Klein{gordon Equation

We analyse three nite diierence approximations of the nonlinear Klein{Gordon equation and show that they are directly related to symplectic mappings. Two of the schemes, the Perring{Skyrme and Ablowitz{Kruskal{Ladik, are long established and the third is a new, higher order accurate scheme. We test the schemes on travelling wave and periodic breather problems over long time intervals, and compa...

The second-order Klein-Gordon field equation

We introduce and discuss the generalized Klein-Gordon second-order partial differential equation in the Robertson-Walker space-time, using the Casimir second-order invariant operator written in hyperspherical coordinates. The de Sitter and anti-de Sitter space-times are recovered by means of a convenient choice of the parameter associated to the space-time curvature. As an application, we discu...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.