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arXiv:0801.0729 · Annual Review of Nuclear and Particle Science

Effective Field Theory and Finite-Density Systems

R. J. Furnstahl, Gautam Rupak, Thomas Schäfer

Published Apr 17, 2008• 31 citations
arXivHTMLPDF

Abstract

This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT; we also survey the varied frontiers of EFT for finite nuclei and nuclear matter.
DOI
10.1146/annurev.nucl.58.110707.171142

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Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.
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Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model‐independent calculations. Particularly interesting are few‐body systems with short‐range interactions and large two‐body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three‐body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four‐body system and N‐boson droplets in two spatial dimensions will also be discussed.
The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD. A common theme is the use of effective field theory (EFT) methods, which exploit the separation of scales in physical systems. At low energies, effective field theory can explain how existing phenomenology emerges from QCD and how to refine it systematically. More generally, the application of EFT methods to many-body problems promises insight into the analytic structure of observables, the identification of new expansion parameters, and a consistent organisation of many-body corrections, with reliable error estimates.