Few-body hierarchy in non-relativistic functional renormalization group equations and a decoupling theorem

TL;DR

This paper demonstrates a hierarchical structure in non-relativistic functional renormalization group equations that enables solving n-body problems independently of higher-body sectors, simplifying few-body quantum field theory analysis.

Contribution

It introduces a decoupling theorem showing that propagators are not renormalized and that the hierarchy allows independent n-body sector solutions.

Findings

Propagators are not renormalized in the few-body limit.

Hierarchical structure enables solving n-body equations independently.

Provides a new approach to non-relativistic quantum field theory analysis.

Abstract

For non-relativistic quantum field theory in the few-body limit with instantaneous interactions it is shown within the functional renormalization group formalism that propagators are not renormalized and that the renormalization group equations of one-particle irreducible vertex functions are governed by a hierarchical structure. This hierarchy allows to solve the equations in the n-body sector without knowledge or assumptions about the m-body sectors where m>n.