Mini review of Poincar\'e invariant quantum theory

TL;DR

This paper reviews Poincaré invariant quantum models for few-particle systems, focusing on their construction, relation to quantum field theory, and practical applications in modeling relativistic quantum dynamics.

Contribution

It provides a comprehensive overview of the construction and application of Poincaré invariant quantum models, highlighting recent developments and practical considerations.

Findings

Demonstrates the construction of dynamical Poincaré group representations

Connects quantum mechanical models to quantum field theory frameworks

Shows applications in realistic interaction modeling and solving dynamical equations

Abstract

We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert spaces, the relation to quantum field theory, the formulation of cluster properties, and practical considerations related to the construction of realistic interactions and the solution of the dynamical equations. Selected applications illustrate the utility of this approach.