Coupling constant

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 characterizes an interaction with two charge-carrying 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.

Coupling constants arise naturally in a quantum field theory. A special role is played in relativistic quantum theories by coupling constants that are dimensionless; i.e., are pure numbers. An example of a dimensionless constant is the fine-structure constant,

where ${\displaystyle e}$ is the charge of an electron, ${\displaystyle \varepsilon _{0}}$ is the permittivity of free space, ${\displaystyle \hbar }$ is the reduced Planck constant and ${\displaystyle c}$ is the speed of light. This constant is proportional to the square of the coupling strength of the charge of an electron to the electromagnetic field.

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