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Quantum field theory |
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It has been suggested that this article be merged into Effective theory . (Discuss) Proposed since November 2024. |
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies). Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects. [1] [2]
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 energy scale in the microscopic theory, then the effective field theory can be seen as an expansion in . The construction of an effective field theory accurate to some power of requires a new set of free parameters at each order of the expansion in . This technique is useful for scattering or other processes where the maximum momentum scale satisfies the condition . 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 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.[ which? ]
The best-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±. The immense success of the Fermi theory was because the W particle 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.
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.
General relativity (GR) itself is expected to be the low energy effective field theory of a full theory of quantum gravity, such as string theory or loop quantum gravity. The expansion scale is the Planck mass. Effective field theories have also been used to simplify problems in general relativity, in particular in calculating the gravitational wave signature of inspiralling finite-sized objects. [3] The most common EFT in GR is non-relativistic general relativity (NRGR), [4] [5] [6] which is similar to the post-Newtonian expansion. [7] Another common GR EFT is the extreme mass ratio (EMR), which in the context of the inspiralling problem is called extreme mass ratio inspiral.
Presently, effective field theories are written for many situations.
A gluon is a type of massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a spin of 1. Through the strong interaction, gluons bind quarks into groups according to quantum chromodynamics (QCD), forming hadrons such as protons and neutrons.
In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.
The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin. Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons and the baryons. In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei. It is part of the first generation of matter, has an electric charge of +2/3 e and a bare mass of 2.2+0.5
−0.4 MeV/c2. Like all quarks, the up quark is an elementary fermion with spin 1/2, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and strong interactions. The antiparticle of the up quark is the up antiquark, which differs from it only in that some of its properties, such as charge have equal magnitude but opposite sign.
The down quark is a type of elementary particle, and a major constituent of matter. The down quark is the second-lightest of all quarks, and combines with other quarks to form composite particles called hadrons. Down quarks are most commonly found in atomic nuclei, where it combines with up quarks to form protons and neutrons. The proton is made of one down quark with two up quarks, and the neutron is made up of two down quarks with one up quark. Because they are found in every single known atom, down quarks are present in all everyday matter that we interact with.
Technicolor theories are models of physics beyond the Standard Model that address electroweak gauge symmetry breaking, the mechanism through which W and Z bosons acquire masses. Early technicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of the strong nuclear force, which inspired their name.
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.
In particle physics, quarkonium is a flavorless meson whose constituents are a heavy quark and its own antiquark, making it both a neutral particle and its own antiparticle. The name "quarkonium" is analogous to positronium, the bound state of electron and anti-electron. The particles are short-lived due to matter-antimatter annihilation.
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.
The QCD vacuum is the quantum vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.
In particle physics, the parton model is a model of hadrons, such as protons and neutrons, proposed by Richard Feynman. It is useful for interpreting the cascades of radiation produced from quantum chromodynamics (QCD) processes and interactions in high-energy particle collisions.
In theoretical physics, the anti-de Sitter/quantum chromodynamics correspondence is a goal to describe quantum chromodynamics (QCD) in terms of a dual gravitational theory, following the principles of the AdS/CFT correspondence in a setup where the quantum field theory is not a conformal field theory.
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is one Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.
Quark–gluon plasma is an interacting localized assembly of quarks and gluons at thermal and chemical (abundance) equilibrium. The word plasma signals that free color charges are allowed. In a 1987 summary, Léon Van Hove pointed out the equivalence of the three terms: quark gluon plasma, quark matter and a new state of matter. Since the temperature is above the Hagedorn temperature—and thus above the scale of light u,d-quark mass—the pressure exhibits the relativistic Stefan-Boltzmann format governed by temperature to the fourth power and many practically massless quark and gluon constituents. It can be said that QGP emerges to be the new phase of strongly interacting matter which manifests its physical properties in terms of nearly free dynamics of practically massless gluons and quarks. Both quarks and gluons must be present in conditions near chemical (yield) equilibrium with their colour charge open for a new state of matter to be referred to as QGP.
In strong interaction physics, light front holography or light front holographic QCD is an approximate version of the theory of quantum chromodynamics (QCD) which results from mapping the gauge theory of QCD to a higher-dimensional anti-de Sitter space (AdS) inspired by the AdS/CFT correspondence proposed for string theory. This procedure makes it possible to find analytic solutions in situations where strong coupling occurs, improving predictions of the masses of hadrons and their internal structure revealed by high-energy accelerator experiments. The most widely used approach to finding approximate solutions to the QCD equations, lattice QCD, has had many successful applications; It is a numerical approach formulated in Euclidean space rather than physical Minkowski space-time.
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is a Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others. The basic formalism is discussed elsewhere.
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is one Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.
In particle physics, the Cornell potential is an effective method to account for the confinement of quarks in quantum chromodynamics (QCD). It was developed by Estia J. Eichten, Kurt Gottfried, Toichiro Kinoshita, John Kogut, Kenneth Lane and Tung-Mow Yan at Cornell University in the 1970s to explain the masses of quarkonium states and account for the relation between the mass and angular momentum of the hadron. The potential has the form:
Color transparency is a phenomenon observed in high-energy particle physics, where hadrons created in a nucleus propagate through that nucleus with less interaction than expected. It suggests that hadrons are first created with a small size in the nucleus, and then grow to their nominal size. Here, color refers to the color charge, the property of quarks and gluons that determines how strongly they interact through the nuclear strong force.