In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). The willingness to question previously held truths and search for new answers resulted in a period of major scientific advancements, now known as the Scientific Revolution. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ...

Nowadays, 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 anaysis. This method also lends credence to the main technique of constructing effective field theories, ie, 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. 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. In physics, the term renormalization refers to a variety of theoretical concepts and computational techniques revolving either around the idea of rescaling transformations, or around the process of removing infinities from the calculated quantities (see also regularization). ... In physics, the adjective renormalizable refers to a theory (usually a quantum field theory) in which all ultraviolet divergences, infinities and other seemingly meaningless results can be cured by the process of renormalization. ...

The most well-known example of an effective field theory is the Fermi theory of beta decay. This 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 In physics, Fermis interaction is an old explanation of the weak force, proposed by Enrico Fermi. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ...

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 which are the W^±. The immense success of the Fermi theory was due to the fact that the W has mass of about 80 GeV, whereas the early experiments were all done at an energy scale of less than 10 MeV. Such a separation of scales, by over 3 orders of magnitude, has not been met in any other situation as yet. Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... Wikipedia does not yet have an article with this exact name. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...

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. BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... A magnet levitating above a high-temperature superconductor with boiling liquid nitrogen underneath demonstrates the Meissner effect. ... Properties The electron is a subatomic particle. ... Hot metal work from a blacksmith In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) in a cloud of electrons. ... A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. ... BCS theory successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ...

Nowadays, 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 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 inverse of the pion mass.
• 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 in which there is a single large momentum exchange, Q, the effect of soft gluons can be summed using the soft and 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.

Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... Particles explode from the collision point of two relativistic velocity (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... Chiral perturbation theory is an effective field theory constructed on a lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In particle physics, pion (short for the Greek pi meson = P middle) is the collective name for three subatomic particles discovered in 1947: Ï€0, Ï€+ and π−. Pions are the lightest mesons. ... In particle physics, Kaons (also called K-mesons and denoted K) are a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. ... In particle physics, Goldstone bosons are bosons that appear in models with spontaneously broken symmetry. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Quarks are one of the two basic constituents of matter in the Standard Model of particle physics. ... Bottom can refer to: In general, the lowermost part (see Wiktionary:Bottom). ... Look up Charm in Wiktionary, the free dictionary Charm can have the following meanings: In the world of paranormal magic, a charm can mean either: An amulet or talisman, or A spell. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... Lattice Quantum Chromodynamics (Lattice QCD) is the theory of quarks and gluons formulated on a space-time lattice. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In particle physics, gluons mediate strong interactions of quarks in quantum chromodynamics. ... Two-dimensional visualization of space-time distortion. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... String theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. ... The Planck mass is the natural unit of mass, denoted by mP. mP = (c / G)1/2 ≈ 2. ... Condensed matter physics (or many-body physics) is the field of physics that deals with the macroscopic physical properties of matter. ...

See also

• Renormalization group
• Quantum field theory

In physics, the term renormalization refers to a variety of theoretical concepts and computational techniques revolving either around the idea of rescaling transformations, or around the process of removing infinities from the calculated quantities (see also regularization). ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ...

References and external links

• 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)[[Category:Statistical mechanics]