Covariant Hamiltonian Dynamics with Negative Energy States

TL;DR

This paper develops a covariant relativistic quantum mechanics framework for bound hadronic systems, incorporating negative energy states to ensure correct Poincaré symmetry and enabling the study of interactions with external probes.

Contribution

It introduces a covariant wave equation framework that includes negative energy states, maintaining Poincaré invariance and facilitating interaction studies.

Findings

Derived nonpathological, covariant wave equations with negative energy states.

Successfully incorporated auxiliary negative energy states for external probe interactions.

Ensured the correct implementation of Poincaré group generators.

Abstract

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincar\'e group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative energy states. Auxiliary negative energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.