Point-Form Hamiltonian Dynamics and Applications

TL;DR

This paper reviews recent advances in point-form relativistic quantum dynamics, highlighting its applications in particle interactions, form factor calculations, and hadron resonance modeling, with potential benefits for quantum field theory quantization.

Contribution

It introduces a Poincare invariant multichannel formalism for relativistic systems and demonstrates its use in calculating form factors and modeling hadron resonances with meson loops.

Findings

Derived electromagnetic form factors for quark-antiquark systems.

Modeled hadron resonances with finite decay widths.

Discussed advantages of hyperboloid quantization in quantum field theory.

Abstract

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincare invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark-antiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space-time hyperboloid could be advantageous.