Fine structure constant
In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted α (the Greek letter alpha), is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. Being a dimensionless quantity, it has the same numerical value of about 1⁄137 in all systems of units. Arnold Sommerfeld introduced the fine-structure constant in 1916.
Some equivalent definitions of α in terms of other fundamental physical constants are:
where:
The definition reflects the relationship between α and the elementary charge e, which equals √4παε0ħc.
In electrostatic cgs units, the unit of electric charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1 and dimensionless. Then the expression of the fine-structure constant, as commonly found in older physics literature, becomes
In natural units, commonly used in high energy physics, where ε0 = c = ħ = 1, the value of the fine-structure constant is
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