The Non-Euclidean Hydrodynamic Klein-Gordon Equation with Perturbative Self-Interacting Field

TL;DR

This paper develops a quantum hydrodynamic model for the Klein-Gordon equation with self-interaction in non-Euclidean spacetime, enabling analysis of meson energy-momentum in gravitational quantum systems.

Contribution

It introduces a generalized non-Euclidean quantum hydrodynamic framework for the Klein-Gordon equation with self-interaction, linking quantum fields to gravity.

Findings

Derivation of quantum energy impulse tensor density for mesons.

Extension of hydrodynamic models to non-Euclidean spacetime.

Potential applications in gravitational quantum systems.

Abstract

In this paper the quantum hydrodynamic approach for the KGE owning a perturbative self-interaction term is developed. The generalized model to non-Euclidean space-time allows to determine the quantum energy impulse tensor density of mesons for the gravitational equation of quantum mechanical systems.