coupling constant

結合定数

関

association constant、binding constant

WordNet

1. steadfast in purpose or devotion or affection; "a man constant in adherence to his ideals"; "a constant lover"; "constant as the northern star"
2. a number representing a quantity assumed to have a fixed value in a specified mathematical context; "the velocity of light is a constant"
3. a quantity that does not vary (同)constant quantity, invariable
4. a mechanical device that serves to connect the ends of adjacent objects (同)coupler
5. the act of pairing a male and female for reproductive purposes; "the casual couplings of adolescents"; "the mating of some species occurs only in the spring" (同)mating, pairing, conjugation, union, sexual union

PrepTutorEJDIC

1. 『不変の』,一定の / 『絶え間のない』,不断の,繰り返される / 《文》〈人が〉心変わりしない;(…に対して)誠実な,貞節な《+『to』+『名』》 / (数学で)常数;(化学・物理分析などにおける)定量
2. 〈U〉連結,結合 / =coupler / 〈U〉〈C〉(電気回路の)結合

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/09/09 13:22:41」(JST)

wiki en

[Wiki en表示]

For the Murray–von Neumann coupling constant, see von Neumann algebra. For the coupling constant in NMR spectroscopy, see Nuclear magnetic resonance spectroscopy and Proton NMR. For coupling strength in bibliometrics, see Bibliographic coupling.

Quantum field theory
Feynman diagram
History
Background Field theory Gauge theory Poincaré symmetry Quantum mechanics Spontaneous symmetry breaking
Symmetries Charge conjugation Crossing Parity Time reversal Symmetry in quantum mechanics
Tools Anomaly Effective field theory Expectation value Faddeev–Popov ghosts Feynman diagram Lattice gauge theory LSZ reduction formula Partition function Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman axioms
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations
Standard Model Electroweak interaction Higgs mechanism Quantum chromodynamics Quantum electrodynamics Yang–Mills theory
Incomplete theories Quantum gravity String theory Supersymmetry Technicolor Theory of everything
Scientists C. D. Anderson P. W. Anderson Bethe Bjorken Bogoliubov Brout Callan Coleman DeWitt Dirac Dyson Englert Fermi Feynman Fierz Fock Fröhlich Glashow Gell-Mann Gross Guralnik Heisenberg Higgs Haag Hagen 't Hooft Jordan Kendall Kibble Lamb Landau Lee Majorana Mills Nambu Nishijima Parisi Polyakov Salam Schwinger Skyrme Sudarshan Tomonaga Veltman Ward Weinberg Weisskopf Weyl Wilczek Wilson Yang Yukawa

In physics, a coupling constant or gauge coupling parameter is a number that determines the strength of the force exerted in an interaction. Usually, the Lagrangian or the Hamiltonian of a system describing an interaction can be separated into a kinetic part and an interaction part. The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant that sits beside an interaction with two matter fields and one photon field (hence the common Feynman diagram with two arrows and one wavy line). Since photons carry electromagnetism, this coupling constant determines how strongly electrons feel such a force and has its value fixed by experiment.

A coupling constant plays an important role in dynamics. For example, one often sets up hierarchies of approximation based on the importance of various coupling constants. In the motion of a large lump of magnetized iron, the magnetic forces may be more important than the gravitational forces because of the relative magnitudes of the coupling constants. However, in classical mechanics one usually makes these decisions directly by comparing forces.

Fine-structure constant

The coupling constant arises naturally in a quantum field theory. A special role is played in relativistic quantum theories by coupling constants which are dimensionless; i.e., are pure numbers. For example, the fine-structure constant,

$\alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}}$

(where $e$ is the charge of an electron, $\varepsilon _{0}$ is the permittivity of free space, $\hbar$ is the reduced Planck constant and $c$ is the speed of light) is such a dimensionless coupling constant that determines the strength of the electromagnetic force on an electron.

Gauge coupling

In a non-Abelian gauge theory, the gauge coupling parameter, $g$, appears in the Lagrangian as

${\frac {1}{4g^{2}}}{\rm {Tr}}\,G_{\mu \nu }G^{\mu \nu }$

(where $G$ is the gauge field tensor) in some conventions. In another widely used convention, $G$ is rescaled so that the coefficient of the kinetic term is 1/4 and $g$ appears in the covariant derivative. This should be understood to be similar to a dimensionless version of the elementary charge defined as

${\sqrt {4\pi \alpha }}\approx 0.30282212\ .$

Weak and strong coupling

In a quantum field theory with a dimensionless coupling constant g, if g is much less than 1 then the theory is said to be weakly coupled. In this case it is well described by an expansion in powers of g, called perturbation theory. If the coupling constant is of order one or larger, the theory is said to be strongly coupled. An example of the latter is the hadronic theory of strong interactions (which is why it is called strong in the first place). In such a case non-perturbative methods have to be used to investigate the theory.

Running coupling

One can probe a quantum field theory at short times or distances by changing the wavelength or momentum, k, of the probe one uses. With a high frequency (i.e., short time) probe, one sees virtual particles taking part in every process. This apparent violation of the conservation of energy can be understood heuristically by examining the uncertainty relation

$\Delta E\Delta t\geq {\frac {\hbar }{2}},$

which allows such violations at short times. The previous remark only applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event is described by "virtual" particles going off the mass shell. Such processes renormalize the coupling and make it dependent on the energy scale, $\mu$, at which one observes the coupling. The dependence of a coupling g(μ) on the energy-scale is known as running of the coupling. The theory of the running of couplings is known as the renormalization group.

Beta functions

Main article: Beta function (physics)

In quantum field theory, a beta function β(g) encodes the running of a coupling parameter, g. It is defined by the relation

$\beta (g)=\mu {\frac {\partial g}{\partial \mu }}={\frac {\partial g}{\partial \ln \mu }},$

where μ is the energy scale of the given physical process. If the beta functions of a quantum field theory vanish, then the theory is scale-invariant.

The coupling parameters of a quantum field theory can flow even if the corresponding classical field theory is scale-invariant. In this case, the non-zero beta function tells us that the classical scale-invariance is anomalous.

QED and the Landau pole

If a beta function is positive, the corresponding coupling increases with increasing energy. An example is quantum electrodynamics (QED), where one finds by using perturbation theory that the beta function is positive. In particular, at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV, one measures α ≈ 1/127.

Moreover, the perturbative beta function tells us that the coupling continues to increase, and QED becomes strongly coupled at high energy. In fact the coupling apparently becomes infinite at some finite energy. This phenomenon was first noted by Lev Landau, and is called the Landau pole. However, one cannot expect the perturbative beta function to give accurate results at strong coupling, and so it is likely that the Landau pole is an artifact of applying perturbation theory in a situation where it is no longer valid. The true scaling behaviour of $\alpha$ at large energies is not known.

QCD and asymptotic freedom

In non-Abelian gauge theories, the beta function can be negative, as first found by Frank Wilczek, David Politzer and David Gross. An example of this is the beta function for quantum chromodynamics (QCD), and as a result the QCD coupling decreases at high energies.

Furthermore, the coupling decreases logarithmically, a phenomenon known as asymptotic freedom (the discovery of which was awarded with the Nobel Prize in Physics in 2004). The coupling decreases approximately as

$\alpha _{s}(k^{2})\ {\stackrel {\mathrm {def} }{=}}\ {\frac {g_{s}^{2}(k^{2})}{4\pi }}\approx {\frac {1}{\beta _{0}\ln \left({\frac {k^{2}}{\Lambda ^{2}}}\right)}},$

where β₀ is a constant computed by Wilczek, Gross and Politzer.

Conversely, the coupling increases with decreasing energy. This means that the coupling becomes large at low energies, and one can no longer rely on perturbation theory.

QCD scale

In quantum chromodynamics (QCD), the quantity Λ is called the QCD scale. The value is

$\Lambda _{MS}=217_{-23}^{+25}{\text{ MeV}}.$

This value is to be used at a scale above the bottom quark mass of about 5 GeV. The meaning of Λ_MS is given in the article on dimensional transmutation.

The proton-to-electron mass ratio is primarily determined by the QCD scale.

String theory

A remarkably different situation exists in string theory since it includes a dilaton. An analysis of the string spectrum shows that this field must be present, either in the bosonic string or the NS-NS sector of the superstring. Using vertex operators, it can be seen that exciting this field is equivalent to adding a term to the action where a scalar field couples to the Ricci scalar. This field is therefore an entire function worth of coupling constants. These coupling constants are not pre-determined, adjustable, or universal parameters; they depend on space and time in a way that is determined dynamically. Sources that describe the string coupling as if it were fixed are usually referring to the vacuum expectation value. This is free to have any value in the bosonic theory where there is no superpotential.

See also

• Canonical quantization, renormalization and dimensional regularization
• Fine structure constant
• Gravitational coupling constant
• Quantum field theory, especially quantum electrodynamics and quantum chromodynamics
• Gluon field, Gluon field strength tensor

References

• An introduction to quantum field theory, by M.E.Peskin and H.D.Schroeder, ISBN 0-201-50397-2

External links

• The Nobel Prize in Physics 2004 – Information for the Public
• Department of Physics and Astronomy of the Georgia State University - Coupling Constants for the Fundamental Forces

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

• 1. 心筋における興奮収縮連関 excitation contraction coupling in myocardium
• 2. 拡張能障害の細胞学的機序 cellular mechanisms of diastolic dysfunction
• 3. 免疫不全症を引き起こすCD3／T細胞受容体複合体疾患 cd3 t cell receptor complex disorders causing immunodeficiency
• 4. サラセミアの臨床症状および診断 clinical manifestations and diagnosis of the thalassemias
• 5. サラセミア症候群の分子病理 molecular pathology of the thalassemic syndromes

English Journal

• Improved detection limits of protein optical fiber biosensors coated with gold nanoparticles.

• Lepinay S, Staff A, Ianoul A, Albert J.Author information Department of Electronics, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6; Department of Chemistry, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6. Electronic address: sandrine.lepinay@carleton.ca.AbstractThe study presented herein investigates a novel arrangement of fiber-optic biosensors based on a tilted fiber Bragg grating (TFBG) coated with noble metal nanoparticles, either gold nanocages (AuNC) or gold nanospheres (AuNS). The biosensors constructed for this study demonstrated increased specificity and lowered detection limits for the target protein than a reference sensor without gold nanoparticles. The sensing film was fabricated by a series of thin-film and monolayer depositions to attach the gold nanoparticles to the surface of the TFBG using only covalent bonds. Though the gold nanoparticle integration had not yet been optimized for the most efficient coverage with minimum number of nanoparticles, binding AuNS and AuNC to the TFBG biosensor decreased the minimum detected target concentrations from 90 nM for the reference sensor, to 11 pM and 8 pM respectively. This improvement of minimum detection is the result of a reduced non-specific absorption onto the gold nanoparticles (by functionalization of the external surface of the gold nanoparticles), and of an optical field enhancement due to coupling between the photonic modes of the optical fiber and the localized surface plasmon resonances (LSPR) of the gold nanoparticles. This coupling also increased the sensitivity of the TFBG biosensor to changes in its local environment. The dissociation constant (Kd) of the target protein was also characterized with our sensing platform and found to be in good agreement with that of previous studies.
• Biosensors & bioelectronics.Biosens Bioelectron.2014 Feb 15;52:337-44. doi: 10.1016/j.bios.2013.08.058. Epub 2013 Sep 14.
• The study presented herein investigates a novel arrangement of fiber-optic biosensors based on a tilted fiber Bragg grating (TFBG) coated with noble metal nanoparticles, either gold nanocages (AuNC) or gold nanospheres (AuNS). The biosensors constructed for this study demonstrated increased specific
• PMID 24080213

• Determination of the geometry change of 5-cyanoindole upon electronic excitation from a combined Franck-Condon/rotational constants fit.

• Stuhlmann B, Gräßle A, Schmitt M.Author information Heinrich-Heine-Universität, Institut für Physikalische Chemie I, D-40225 Düsseldorf, Germany. mschmitt@uni-duesseldorf.de.AbstractThe geometry change of 5-cyanoindole upon electronic excitation from the ground to the lowest excited singlet state has been determined from a combined fit of the rotational constant changes upon excitation and the vibronic intensities in various fluorescence emission spectra using the Franck-Condon principle. The so determined geometry change is compared to the results of ab initio calculations and points to an excited state geometry, which is La-like in the nomenclature of Platt. A mode selective coupling of vibronic bands to higher-lying excited states is discussed on the basis of Herzberg-Teller contributions to the Frank-Condon intensities.
• Physical chemistry chemical physics : PCCP.Phys Chem Chem Phys.2014 Jan 21;16(3):899-905. doi: 10.1039/c3cp51795k. Epub 2013 Sep 24.
• The geometry change of 5-cyanoindole upon electronic excitation from the ground to the lowest excited singlet state has been determined from a combined fit of the rotational constant changes upon excitation and the vibronic intensities in various fluorescence emission spectra using the Franck-Condon
• PMID 24060846

• Highly sensitive detection of molecular interactions with plasmonic optical fiber grating sensors.

• Voisin V, Pilate J, Damman P, Mégret P, Caucheteur C.Author information Electromagnetism and Telecommunications Department, University of Mons, Mons, Belgium.AbstractSurface Plasmon resonance (SPR) optical fiber biosensors constitute a miniaturized counterpart to the bulky prism configuration and offer remote operation in very small volumes of analyte. They are a cost-effective and relatively straightforward technique to yield in situ (or even possibly in vivo) molecular detection. The biosensor configuration reported in this work uses nanometric-scale gold-coated tilted fiber Bragg gratings (TFBGs) interrogated by light polarized radially to the optical fiber outer surface, so as to maximize the optical coupling with the SPR. These gratings were recently associated to aptamers to assess their label-free biorecognition capability in buffer and serum solutions. In this work, using the well-acknowledged biotin-streptavidin pair as a benchmark, we go forward in the demonstration of their unique sensitivity. In addition to the monitoring of the self-assembled monolayer (SAM) in real time, we report an unprecedented limit of detection (LOD) as low as 2 pM. Finally, an immunosensing experiment is realized with human transferrin (dissociation constant Kd~10(-8) M(-1)). It allows to assess both the reversibility and the robustness of the SPR-TFBG biosensors and to confirm their high sensitivity.
• Biosensors & bioelectronics.Biosens Bioelectron.2014 Jan 15;51:249-54. doi: 10.1016/j.bios.2013.07.030. Epub 2013 Jul 19.
• Surface Plasmon resonance (SPR) optical fiber biosensors constitute a miniaturized counterpart to the bulky prism configuration and offer remote operation in very small volumes of analyte. They are a cost-effective and relatively straightforward technique to yield in situ (or even possibly in vivo)
• PMID 23973934

Japanese Journal

• First-Principles Momentum Dependent Local Ansatz Approach to the Ground-State Properties of Iron-Group Transition Metals

• Journal of the Physical Society of Japan 85(8), 084708-1-8, 2016-07-25
• NAID 40020906474

• Superconductivity in a Misfit Phase That Combines the Topological Crystalline Insulator Pb₁₋xSn[x]Se with the CDW-Bearing Transition Metal Dichalcogenide TiSe₂

• Journal of the Physical Society of Japan 85(6), 064705-1-5, 2016-05-13
• NAID 40020851924

• Phenomenology in minimal theory of massive gravity

• Journal of Cosmology and Astroparticle Physics 2016, 2016-04-15
• NAID 120005841439

Related Pictures

---

★リンクテーブル★

リンク元	「association constant」
関連記事	「constant」「coupling」

「association constant」

　　[★]

• 会合定数、結合定数

関

binding constant、coupling constant

「constant」

　　[★]

• adj.

• 定常性の、一定の、普遍の

• n.

• 定数

関

constancy、constantly、invariable、invariably、stationary、uniform

　 　 　 　

「coupling」

　　[★]

• 共役、連関、配偶、カップリング

関

association、conjugate、conjugated、conjugation、couple、linkage