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## Effective field theoryIn physics, an ## Additional recommended knowledgePresently, effective field theories are discussed in the context of the renormalization group (RG) where the process of The most well-known example of an effective field theory is the Fermi theory of beta decay. This theory was developed during the early study of weak decays of nuclei when only the hadrons and leptons undergoing weak decay were known. The typical reactions studied were: This theory posited a pointlike interaction between the four fermions involved in these reactions. The theory had great phenomenological success and was eventually understood to arise from the gauge theory of electroweak interactions, which forms a part of the standard model of particle physics. In this more fundamental theory, the interactions are mediated by a flavour-changing gauge boson, the W Another famous example is the BCS theory of superconductivity. In this case the underlying theory is the theory of electrons in a metal interacting with lattice vibrations called phonons. The phonons cause attractive interactions between appropriate electrons, causing them to form Cooper pairs. The length scale of these pairs is much larger than the wavelength of phonons. As a result, it is possible to neglect the dynamics of phonons and construct a theory in which two electrons interact at a point. This is the BCS theory, which has had remarkable success in describing and predicting the results of experiments. Presently, effective field theories are written for many situations. - One major branch of nuclear physics is quantum hadrodynamics, where the interactions of hadrons are treated as a field theory, which one hopes to derive from quantum chromodynamics, the true underlying theory, in the future. Due to the smaller separation of length scales here, this effective theory has some classificatory power, but not the spectacular success of the Fermi theory.
- In particle physics the effective field theory of QCD called chiral perturbation theory has had better success. This theory deals with the interactions of hadrons with pions or kaons, which are the Goldstone bosons of spontaneous chiral symmetry breaking. The expansion parameter is the pion energy/momentum.
- For hadrons containing one heavy quark (such as the bottom or charm), an effective field theory which expands in powers of the quark mass, called the heavy-quark effective theory (HQET), has been found useful.
- For hadrons containing two heavy quarks, an effective field theory which expands in powers of the relative velocity of the heavy quarks, called non-relativistic QCD (NRQCD), has been found useful, especially when used in conjunctions with lattice QCD.
- For hadron reactions with light energetic (collinear) particles, the interactions with low-energetic (soft) degrees of freedom are described by the soft-collinear effective theory (SCET).
- General relativity is expected to be the low energy effective theory of a full theory of quantum gravity, such as string theory. The expansion scale is the Planck mass.
- All of condensed matter physics consists of writing effective field theories for the particular property of matter being studied.
- Effective field theories have also been used to simplify problems in General Relativity (NRGR). In particular in calculating post-Newtonian corrections to the gravity wave signature of inspiralling finite-sized objects. [1]
## See also- Renormalization group
- Quantum field theory
## References and external links- Effective field theories, reduction and scientific explanation, by S. Hartmann,
*Studies in History and Philosophy of Modern Physics***32B**, 267-304 (2001). - On the foundations of chiral perturbation theory, H. Leutwyler (Annals of Physics, v 235, 1994, p 165-203)
- Aspects of heavy quark theory, by I. Bigi, M. Shifman and N. Uraltsev (Annual Reviews of Nuclear and Particle Science, v 47, 1997, p 591-661)
- Effective field theory (Interactions, Symmetry Breaking and Effective Fields - from Quarks to Nuclei. an Internet Lecture by Jacek Dobaczewski)
Categories: Statistical mechanics | Condensed matter physics |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Effective_field_theory". A list of authors is available in Wikipedia. |