An **coupling constant** (or an
interaction constant) is a parameter in the field theory, which determines the
relative strength of interaction between particles or fields. In the quantum
field theory the coupling constants are associated with the vertices of the
corresponding Feynman diagrams. Dimensionless parameters are used as coupling
constants, as well as the quantities associated with them that characterize the
interaction and have dimensions. The examples are the dimensionless fine structure constant of electromagnetic
interaction and the electric elementary charge, measured in coulombs (C).

- 1 Comparison of interactions

- 1.1 Gravitational
interaction
- 1.2 Weak
interaction
- 1.3 Electromagnetic
interaction
- 1.4 Strong
interaction

- 2 The constants in the quantum
field theory
- 3 The constants in other theories

- 3.1 String
theory
- 3.2 Strong
gravitation
- 3.3 Interactions
at the level of stars

- 4 References
- 5 See also
- 6 Additional references
- 7 External links

If we choose an object that
participates in all the four fundamental interactions, the values of the
dimensionless coupling constants of this object, found according to the general
rule, will show the relative strength of these interactions. At the level of
elementary particles a proton is most commonly used as such an object. The
basic energy for comparison of interactions is the electromagnetic energy of a
photon, which equals by definition:

where is
the Planck constant, is
the speed of light, is
the photon wavelength. The choice of the photon energy is not accidental, since
the basis of the modern science is the wave representation based on
electromagnetic waves. All the main measurements, including length, time and
energy, are made with the help of them.

The energy of gravitational
interaction between two protons is given by:

where is
the gravitational constant, is the proton mass, is
the distance between the protons’ centers.

If we assume that the distance and the electromagnetic photon’s wavelength are related by the formula , then the ratio of the absolute value of
the gravitational interaction energy to the photon’s energy gives the
dimensionless coupling constant:

where is
the Dirac constant.

The energy associated with the
weak interaction can be represented as follows:

where is
the effective charge of weak interaction, is
the mass of virtual particles that are considered the carrier particles for
weak interaction (W and Z bosons). The square of the effective charge of weak
interaction for the proton is expressed in terms of the Fermi constant J•m^{3} and the proton mass:

At sufficiently small distances the
exponent in the weak interaction energy can be neglected. In this case, the
dimensionless coupling constant of weak interaction is determined as follows:

The electromagnetic interaction
of two fixed protons is described by the electrostatic energy:

where is
the elementary charge, is
the vacuum permittivity.

The ratio of this energy to the
photon energy determines the electromagnetic coupling
constant, known as the fine structure
constant:

At the level of hadrons, the
strong interaction is regarded in the Standard Model of elementary particle
physics as “residual” interaction of quarks that are part of hadrons. It is
assumed that gluons as the carriers of strong interaction generate virtual
mesons in the space between the hadrons. In the pion-nucleon model of Yukawa
interaction, the nuclear forces between the nucleons are explained as a result
of the virtual pions exchange, and the interaction
energy is as follows:

where is
the effective charge of the pseudoscalar pion-nucleon
interaction, is the pion mass.

The dimensionless strong
interaction coupling constant is:

The interaction effects in the
field theory are often determined with the help of perturbation theory, in
which the expansion of functions in the equations in powers of the coupling
constant is performed. Usually for all interactions, except the strong
interaction, the coupling constant is significantly less than unity. This makes
the use of the perturbation theory effective, since the contribution from the
highest terms of expansions decreases rapidly and calculating them becomes
unnecessary. In case of strong interaction the perturbation theory becomes
unsuitable and other methods of calculation are required.

One of the predictions of the
quantum field theory is the so-called effect of “floating constants”, according
to which the coupling constants change slowly with increasing of the energy,
transferred during the interaction between the particles. Thus, the
electromagnetic coupling constant increases and the strong interaction constant
coupling decreases with the increase of energy. In Quantum Chromodynamics a
special strong interaction coupling constant is introduced for the quarks:

where is
the effective color charge of the quark, emitting virtual gluons for the
interaction with other quarks.

As the distance between the
quarks decreases, due to the collisions of high energy particles, it is
expected the log reduction of and
the weakening of strong interaction (the effect of asymptotic freedom of
quarks). ^{[1]} At the scale of the transferred energy
of the order of the Z boson’s mass-energy (91.19 GeV) it was found that ^{[2]} At the same energy scale the
electromagnetic interaction coupling constant increases up to the value of the
order of 1/127 instead of ≈1/137 at low energies. It is assumed that at higher
energies, of the order of 10^{18} GeV, the values of the coupling
constants of gravitational, weak, electromagnetic and strong interactions of
particles will become closer and even become approximately equal to each other.

In the string theory, the
coupling constants are considered not as constant but as dynamic quantities. In
particular, in the same theory at low energies it seems that the strings move
in ten dimensions and at high energies — in eleven. The changing number of
dimensions is accompanied by a change in the coupling constants. ^{[3]}

Strong gravitation together with the gravitational torsion field and
electromagnetic forces are considered the main components of strong interaction
in the gravitational model of strong
interaction. In this model, instead of considering interactions of quarks
and gluons, only two fundamental fields (gravitational and electromagnetic
fields) are taken into account, which act in the charged matter of elementary
particles that has mass, as well as in the space between them. In this case,
quarks and gluons, according to the model
of quark quasiparticles, are considered not as real particles but as
quasiparticles, reflecting the quantum properties and symmetry, inherent in
hadronic matter. This approach significantly reduces the number (the record
number for a physical theory) of unproved but postulated free parameters that
exist in the standard model of elementary particle physics, where there are at
least 19 parameters of this kind.

Another consequence is that the
weak and strong interactions are not considered as independent field
interactions. The strong interaction is reduced to combinations of
gravitational and electromagnetic forces, in which an important role is played
by the interactions’ delay effects (dipole and orbital torsion fields and
magnetic forces). Accordingly, the strong coupling constant is determined by
analogy with the gravitational interaction coupling constant: ^{[4]}

where is
the strong gravitational constant, is the electron mass, is a coefficient, which is equal to 0.26 for the interaction of two
nucleons and is tending to 1 for bodies with lower matter density.

As for the weak interaction, it
is assumed to be the result of the transformation of matter of elementary
particles, which occurs due to the reactions of weak interaction, but at a
deeper level of matter. The examples of weak interaction with nucleons are
considered in the substantial neutron model
and the substantial proton model.

Among the stellar constants, describing the quantization of parameters of cosmic systems
in the hydrogen system of stars, there
are two dimensionless constants. One of them determines the stellar fine
structure constant and the other determines the relative
strength of interaction between two stars. In case of the hydrogen system of
the magnetar and the disks near it these constants equal:

where C is the electric charge of the magnetar,
based on its similarity with the proton, J∙s is the stellar Dirac constant
for the system with the magnetar, m/s is the stellar speed as the characteristic speed of the matter particles
in a typical neutron star, kg is the mass of the magnetar, kg is the mass of the disk, which is the electron’s analogue at the level
of stars.

Due to the SPФ symmetry and the similarity of matter levels, the values of
the dimensionless coupling constants are the same both at the atomic level and
at the level of stars.

- Wilczek, F.; Gross, D.J. (1973). "Asymptotically
Free Gauge Theories". Phys. Rev. D 8 (10): 3633.
doi:10.1103/PhysRevD.8.3633.
- Yao W-M et al. (Particle Data Group) J. Phys. G: Nucl. Part. Phys. Vol. 33, P. 1 (2006).
- Гросс,
Дэвид. Грядущие революции в фундаментальной физике.
Проект «Элементы», вторые публичные лекции по физике (25.04.2006).
- Comments to the
book: Fedosin S.G. Fizicheskie teorii i beskonechnaia
vlozhennost’ materii. –
Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref.
289. ISBN 978-5-9901951-1-0. (in Russian).

- Model of quark quasiparticles
- Substantial neutron model
- Substantial proton model
- Substantial electron model
- Infinite Hierarchical Nesting of Matter
- Similarity of matter levels
- SPФ symmetry
- Stellar constants
- Quantization of parameters of cosmic
systems
- Discreteness of stellar parameters
- Hydrogen system
- Strong gravitation
- Gravitational torsion field
- Gravitational
model of strong interaction
- Quarks
- Physics/Essays/Fedosin/Magnetic
coupling constant

- Р. Маршак, Э. Судершан.
*Введение в физику элементарных частиц*, 1962. - M.E.
Peskin and H.D. Schroeder.
*An introduction to quantum field theory*, ISBN 0-201-50397-2.