Effective field theory
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Quantum field theory |
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History |
In
The renormalization group
Presently, effective field theories are discussed in the context of the renormalization group (RG) where the process of integrating out short distance degrees of freedom is made systematic. Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through an RG analysis. This method also lends credence to the main technique of constructing effective field theories, through the analysis of symmetries. If there is a single mass scale M in the microscopic theory, then the effective field theory can be seen as an expansion in 1/M. The construction of an effective field theory accurate to some power of 1/M requires a new set of free parameters at each order of the expansion in 1/M. This technique is useful for scattering or other processes where the maximum momentum scale k satisfies the condition k/M≪1. Since effective field theories are not valid at small length scales, they need not be renormalizable. Indeed, the ever expanding number of parameters at each order in 1/M required for an effective field theory means that they are generally not renormalizable in the same sense as quantum electrodynamics which requires only the renormalization of two parameters.
Examples of effective field theories
Fermi theory of beta decay
The best-known example of an effective field theory is the
This theory posited a pointlike interaction between the four
BCS theory of superconductivity
Another famous example is the BCS theory of superconductivity. Here the underlying theory is the theory of electrons in a metal interacting with lattice vibrations called phonons. The phonons cause attractive interactions between some electrons, causing them to form Cooper pairs. The length scale of these pairs is much larger than the wavelength of phonons, making it possible to neglect the dynamics of phonons and construct a theory in which two electrons effectively interact at a point. This theory has had remarkable success in describing and predicting the results of experiments on superconductivity.
Effective field theories in gravity
Other examples
Presently, effective field theories are written for many situations.
- One major branch of electromagnetic force. 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 spontaneous chiral symmetry breaking. The expansion parameter is the pionenergy/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 collinear) particles, the interactions with low-energetic (soft) degrees of freedom are described by the soft-collinear effective theory(SCET).
- Much of condensed matter physics consists of writing effective field theories for the particular property of matter being studied.
- Hydrodynamics can also be treated using Effective Field Theories[9]
See also
- Form factor (quantum field theory)
- Renormalization group
- Quantum field theory
- Quantum triviality
- Ginzburg–Landau theory
References
Books
- A.A. Petrov and A. Blechman, ‘’Effective Field Theories,’’ Singapore: World Scientific (2016). ISBN 978-981-4434-92-8
- C.P. Burgess, ‘’Introduction to Effective Field Theory,‘’ Cambridge University Press (2020). ISBN 978-052-1195-47-8
External links
- Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (1998). "Effective Field Theory". arXiv:hep-ph/9806303.
- Hartmann, Stephan (2001). "Effective Field Theories, Reductionism and Scientific Explanation" (PDF). Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 32 (2): 267–304. .
- Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (1997). "Aspects of Heavy Quark Theory". S2CID 13843227.
- Effective field theory (Interactions, Symmetry Breaking and Effective Fields - from Quarks to Nuclei. an Internet Lecture by Jacek Dobaczewski)