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Related Experiment Video

Updated: Jun 1, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Renormalization group for non-relativistic fermions.

¹Sloane Physics Laboratory, Yale University, New Haven, CT 06520, USA. r.shankar@yale.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|June 8, 2011

Summary

The renormalization group explains Fermi liquid theory and its instabilities for non-relativistic fermions. This framework applies to nuclear matter, quark matter, and quantum dots.

Area of Science:

Condensed Matter Physics
Quantum Field Theory

Background:

The renormalization group (RG) is a powerful tool for understanding systems with many interacting particles.
Non-relativistic fermions at finite density present complex many-body problems.

Purpose of the Study:

To introduce the renormalization group approach for non-relativistic fermions at finite density.
To demonstrate how Landau's Fermi liquid theory emerges as a stable fixed point within this framework.
To explore instabilities of the Fermi liquid as relevant perturbations.

Main Methods:

Application of the renormalization group technique to a system of non-relativistic fermions.
Identification of fixed points and analysis of their stability (marginal and relevant couplings).

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Last Updated: Jun 1, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Main Results:

Landau's Fermi liquid theory is shown to be a fixed point of the renormalization group flow.
The Landau parameters are identified as marginal couplings.
Instabilities of the Fermi liquid are characterized as relevant perturbations.

Conclusions:

The renormalization group provides a unified framework for understanding Fermi liquid behavior and its instabilities.
The approach has potential applications in diverse areas such as nuclear matter, quark matter, and quantum dots.