Representation Structure of the $SL(2, \mathbb{C})$ Acting in the Hilbert Space of the Quantum Coulomb Field

TL;DR

This paper provides a comprehensive description of how the $SL(2, \\mathbb{C})$ group acts within the Hilbert space of the quantum Coulomb field and offers a constructive proof of the quantum Coulomb field axioms.

Contribution

It offers the first complete characterization of the $SL(2, \\mathbb{C})$ representation in this context and validates the foundational axioms of the quantum Coulomb field theory.

Findings

Explicit $SL(2, \\mathbb{C})$ representation structure derived

Constructive proof of quantum Coulomb field axioms provided

Enhanced understanding of the quantum Coulomb field's mathematical framework

Abstract

We give a complete description of the representation of $SL(2,\mathbb{C})$ acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum theory of the Coulomb field.