Large-N Theory from the Axiomatic Point of View

TL;DR

This paper constructs a large-N quantum field theory model that satisfies axiomatic principles, demonstrating nontrivial phenomena like scattering, bound states, and divergences, thus providing a rigorous foundation for infinite-field theories.

Contribution

It develops an axiomatic framework for large-N theories, showing they can be consistent, nontrivial, and include complex phenomena such as divergences and bound states.

Findings

Model obeys Wightman axioms and invariance under boosts

Includes scattering processes, bound states, unstable particles

Addresses divergences like volume and wave function renormalization

Abstract

The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations) and to be nontrivial (there are scattering processes, bound states, unstable particles etc). The considered class of exactly solvable relativistic quantum models involves good examples of theories containing such difficulties as volume divergences associated with the Haag theorem, Stueckelberg divergences and infinite renormalization of the wave function.