Tensor of the energy - momentum and forbiddance of the classical Lump

TL;DR

This paper proves that static solutions of massive classical fields cannot exist in Minkowski spacetime with more than two dimensions, extending Derrick's theorem using energy-momentum tensors and advanced mathematical models.

Contribution

It generalizes the forbiddance of static localized classical fields to higher dimensions and employs novel tensor methods and models for analyzing Yang-Mills lumps.

Findings

Static solutions are forbidden in higher-dimensional Minkowski space.

The approach extends Derrick's theorem using energy-momentum tensors.

Application of advanced mathematical models to field solutions.

Abstract

We show that the static solutions of massive classical fields are forbidden in the Minkowski space time with dimensions higher than $2$. The purpose of this study is to generalize the forbiddance of the time independent localized classical fields in general space time. We generalize the Derrick theorem as unstable stationary localized solutions for the nonlinear wave equation or the nonlinear Klein - Gordon equation in Minkowski space time. Our approach employs the tensor of the energy - momentum based on Weber's method. We exploite the Bateman - Caldilora - Kanai model and the Deser method for the research of the Yang - Mills Lumps as massive solutions. We also use Riemann's coordinates for parametrization of tangent space as a local framework. The important point of this article is the homomorphism between the Minkowsian and pseudo Riemann's manifolds.