In physics, a coupling constant, usually denoted g, 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.
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 are 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.
Read more about Coupling Constant: Fine-structure Constant, Gauge Coupling, Weak and Strong Coupling, Running Coupling, Beta Functions, QED and The Landau Pole, QCD and Asymptotic Freedom, QCD Scale, String Theory
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