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,...

Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets filled with oscillations whose amplitudes decrease in the Gaussian way with distance from a point running with group velocity along a straight line. The solutio...

We derive the long-time decay in weighted norms for solutions of the discrete 3D Schrödinger and Klein-Gordon equations.

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considere...

Classical nonlocal field models consisting of probability densities over functions defined everywhere on Minkowski space are constructed, using functional methods. These models are equivalent to states of the quantized real Klein-Gordon field in the sense that the marginal probability density over real functions defined everywhere on a 3dimensional hyperplane S, at all times and for all Lorentz...

The change of signature of a metric is explained using simple examples and methods. The Klein-Gordon field on a signature-changing background is discussed, and it is shown how the approach of Dray et al. can be corrected to ensure that the KleinGordon equation holds. Isotropic cosmologies are discussed, and it is shown how the approach of Ellis et al. can be corrected to ensure that the Einstei...