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 electric constant.

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.