Single particles and composite systems in a mathematically rigorous formulation of relativistic quantum field theory

TL;DR

This paper presents a rigorous mathematical formulation of relativistic quantum field theory using well-defined functionals and operator fields, enabling a clear description of particles, interactions, and bound states.

Contribution

It introduces a mathematically rigorous framework that avoids Haag's theorem and allows direct definitions of wave functions and many-body bound states.

Findings

Fock space expansion of renormalized fields is well-defined

Interaction picture exists within this formalism

Framework enables description of bound-state systems

Abstract

We define quantum field theory by taking the Lagrangian action to be given as a sequence of mathematically well-defined functionals written in terms of operator fields fulfilling given \hbox{local} commutation relations. The renormalized solution fields have a fully defined Fock space expansion and are \hbox{multi-local}; thus Haag's theorem does not apply, i.e., the interaction picture exists. Also, the formalism allows immediately the definition of a wave function and the description of many-body bound-state systems.