Dynamical Adjustment of Propagators in Renormalization Group Flows

TL;DR

This paper introduces a novel class of continuous renormalization group flows with dynamically adjusted propagators, enabling better handling of self-energy effects and Fermi surface evolution in quantum field theories.

Contribution

It presents a new method for dynamical propagator adjustment in RG flows, allowing inclusion of self-energy effects and natural Fermi surface flow definition without counterterms.

Findings

Propagator adjustment influences strong-coupling behavior.

Flows can include self-energy effects nontrivially.

Counterterms can be derived from the new flows.

Abstract

A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self--energy effects nontrivially in the denominator of the propagator and to adapt the scale decomposition to a moving singularity, and hence to define flows of Fermi surfaces in a natural way. These flows require no counterterms, but the counterterms used in earlier treatments can be constructed using them. The influence of propagator adjustment on the strong--coupling behaviour of flows is examined for a simple example, and some conclusions about the strong coupling behaviour of renormalization group flows are drawn.