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The term "coupling constant" comes from field theory. In field theory, all matter and radiation is studied in terms of fields.

Fields are quantities whose value depends on position in space, as well as time.

Fields have kinetic energy. This appears in the equations in the form of time variation of those fields.

Fields also have "internal energy" due to spatial gradients of their values.

They also have interactions with other fields, that appear as proportional to the product of one field with another. The constant of proportionality is called "coupling constant", and how big it is tells you how strongly they interact with each other.

Fields also have self-interactions. These appear as powers of the field itself. Those also have coupling constants.

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