It is proved that density plays a crucial role in the structure of quantum field theory. The Dirac and the Klein-Gordon equations are examined. The results prove that the Dirac equation is consistent with density related requirements whereas the Klein-Gordon equation fails to do that. Experimental data support these conclusions.

With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction u4 we define the Wick kernel of the interacting quantum field in four-dimensional space-time and consider its properties. In particular, the diagonal of this Wick kernel is (real) solutions of the classical nonlinear Klein-Gordon equation with the interaction u4.

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 ...

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 give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positive-frequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequence...

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positivefrequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequences...

We develop a general theory to treat the linear stability of certain special solutions of second order in time evolutionary PDEs. We apply these results to standing waves of the following problems: the Klein-Gordon equation, for which we consider both ground states and certain excited states, the Klein-Gordon-Zakharov system and the beam equation. We also discuss possible applications to some n...

We study evaporation process of black strings which are typical examples of Kaluza-Klein black holes. Taking into account the backreaction of the Hawking radiation, we deduce the evolution equation for the radion field. By solving the evolution equation, we find that the shape of the internal space is necked by the Hawking radiation and the amount of the deformation becomes large as the evapora...