# General Aspects of Effective Field Theories and Few-Body Applications

@article{Hammer2016GeneralAO,
title={General Aspects of Effective Field Theories and Few-Body Applications},
author={Hans-Werner Hammer and Sebastian Konig},
journal={Lecture Notes in Physics},
year={2016},
volume={936},
pages={93-153}
}
• Published 2016
• Physics
• Lecture Notes in Physics
Effective field theory provides a powerful framework to exploit a separation of scales in physical systems. In these lectures, we discuss some general aspects of effective field theories and their application to few-body physics. In particular, we consider an effective field theory for non-relativistic particles with resonant short-range interactions where certain parts of the interaction need to be treated nonperturbatively. As an application, we discuss the so-called pionless effective field… Expand

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#### References

SHOWING 1-10 OF 34 REFERENCES
More effective field theory for non-relativistic scattering
An effective field theory treatment of nucleon-nucleon scattering at low energy shows much promise and could prove to be a useful tool in the study of nuclear matter at both ordinary and extremeExpand
EFFECTIVE FIELD THEORY FOR FEW-NUCLEON SYSTEMS*
• Physics
• 2002
▪ Abstract We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed toExpand
Narrow resonances in effective field theory
• Physics
• 2003
We discuss the power counting for effective field theories with narrow resonances near a two-body threshold. Close to threshold, the effective field theory is perturbative and only one combination ofExpand
Effective theory of the triton
• Physics
• 2000
Abstract We apply the effective field theory approach to the three-nucleon system. In particular, we consider S=1/2 neutron–deuteron scattering and the triton. We show that in this channel a uniqueExpand
Effective field theory of short-range forces
Abstract The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that theExpand
Nucleon-nucleon scattering from effective field theory
• Physics
• 1996
We perform a non-perturbative calculation of the 1S0 NN scattering amplitude, using an effective field theory (EFT) expansion. The expansion we advocate is a modification of what has been usedExpand
Effective field theory for halo nuclei: shallow p-wave states
• Physics
• 2002
Halo nuclei are a promising new arena for studies based on effective field theory (EFT). We develop an EFT for shallow p-wave states and discuss the application to elastic nα scattering. In contrastExpand
Renormalization of the Three-Body System with Short-Range Interactions
• Physics
• 1999
We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The problem becomes nonperturbative at momenta of the order of the inverse of the two-body scatteringExpand
Chiral perturbation theory to one loop
• Physics
• 1984
* in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian. The low energy representation of several Green’s functions and formExpand
The three-boson system with short-range interactions
• Physics
• 1998
Abstract We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-bodyExpand