# Effective field theory

An effective field theory (EFT) is a type of physical approximation theory for a field theory. The effective field theory applies to a particular field theory and includes the appropriate degrees of freedom for a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies).

## Quotes

* It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, aardvarks, molecules, atoms and nuclei are very different sizes, and are held together with very different binding energies. Happily enough, it is another fact of life that we don’t need to understand what is going on at all scales at once in order to figure out how Nature works at a particular scale. Like good musicians, good physicists know which scales are relevant for which compositions. The mathematical framework which we use to describe nature — quantum field theory — itself shares this basic feature of Nature: it automatically limits the role which smaller distance scales can play in the description of larger objects. This property has many practical applications, since a systematic identification of how scales enter into calculations provides an important tool for analyzing systems which have two very different scales, m ≪ M. In these systems it is usually profitable to expand quantities in the powers of the small parameter, m/M, and the earlier this is done in a calculation, the more it is simplified.
** C. P. Burgess, (2007). "Introduction to Effective Field Theory". arXiv:hep-th/0701053v2. (quote from 1st page)
* ... Imagine you have an image with enormous resolution, but all you really need to know is whether a giant gorilla sits at the center of the image. To that end, a low-resolution picture would suffice. Effective-field theory is the tool a nuclear physicist would use to controllably blur the picture, reduce its complexity, and make the problem computationally tractable. Effective-field theory averages out QCD interactions’ short-range components not relevant to the physics of nuclei, and it provides a form of the NN force using parameters that can be determined directly from QCD. The resulting NN force can then be used to solve the nuclear many-body problem and calculate all relevant nuclear properties
** Filomena M. Nunes, (May 2021)"Why are theorists excited about exotic nuclei?". Physics Today 74 (5): 35–40. (quote from p. 36)
* What makes a field theory effective? We shall argue in this book that the way calculations are set up in EFTs makes them the most natural and convenient tools to address multi scale problems. Problems with separated scales often appear in Nature, and we intuitively know that it is most convenient to only work with degrees of freedom that are relevant for a particular scale — otherwise the problem quickly becomes intractable! You never worry about physics of the atoms when designing bridges, nor try to track each and every molecule of a gas through phase space; you instead define some "macroscopic" variables, and once you know how to relate those variables to the more "fundamental" laws, you can stop thinking about those cases and focus only on the relevant large-scale physics. EFT techniques codify this principle when working with problems in quantum field theory.
** Alexey A. Petrov and Andrew E. Blechman, "Introduction". Effective Field Theories. World Scientific. 18 November 2015. p. 1. ISBN 978-981-4434-93-5.

## See also

* Force field (physics)
* Quantum field theory
* String theory

## External links

Encyclopedic article on Effective field theory on Wikipedia