Review of the N-quantum Approach to Bound States

TL;DR

This paper reviews the N-quantum approach to solving quantum field theories, emphasizing the treatment of bound states through asymptotic fields, with an example application to the nonrelativistic hydrogen atom.

Contribution

It introduces a novel operator-based method for bound states in quantum field theories using asymptotic fields, applicable to both nonrelativistic and relativistic cases.

Findings

Demonstrated the method on the hydrogen atom

Outlined future applications to relativistic bound states

Provided a framework for operator techniques in quantum field theory

Abstract

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.