Editing Fine-structure constant (section)

== Definition ==
In terms of other [[physical constant]]s, {{mvar|α}} may be defined as:<ref name="CODATA 2018">
{{cite web |last1=Mohr |first1=P. J. |last2=Taylor |first2=B. N. |last3=Newell |first3=D. B. |year=2019 |title=Fine-structure constant |work=CODATA Internationally recommended 2018 values of the fundamental physical constants |publisher=[[National Institute of Standards and Technology]] |url=https://physics.nist.gov/cgi-bin/cuu/Value?alph}}</ref>
<math display="block">\alpha = \frac{e^2}{2 \varepsilon_0 h c} = \frac{e^2}{4 \pi \varepsilon_0 \hbar c} ,</math>
where
* {{mvar|e}} is the [[elementary charge]] ({{physconst|e}});
* {{mvar|h}} is the [[Planck constant]] ({{physconst|h}});
* {{mvar|ħ}} is the [[reduced Planck constant]], {{math|1=''ħ'' = ''h''/2''π''}} ({{physconst|hbar}})
* {{mvar|c}} is the [[speed of light]] ({{physconst|c}});
* {{mvar|ε}}{{sub|0}} is the [[Vacuum permittivity|electric constant]] ({{physconst|eps0}}).

Since the [[2019 revision of the SI]], the only quantity in this list that does not have an exact value in [[International System of Units|SI]] units is the electric constant (vacuum permittivity).

=== Alternative systems of units ===
The electrostatic [[CGS]] system implicitly sets {{math|1=4''πε''{{sub|0}} = 1}}, as commonly found in older physics literature, where the expression of the fine-structure constant becomes
<math display="block"> \alpha = \frac{e^2}{\hbar c} .</math>

A nondimensionalised system [[natural units|commonly used in high energy physics]] sets {{math|1=''ε''{{sub|0}} = ''c'' = ''ħ'' = 1}}, where the expression for the fine-structure constant becomes<ref>
{{cite book |last1=Peskin |first1=M. |last2=Schroeder |first2=D. |year=1995 |title=An Introduction to Quantum Field Theory |publisher=[[Westview Press]] |isbn=978-0-201-50397-5 |page=[https://archive.org/details/introductiontoqu0000pesk/page/125 125] |url=https://archive.org/details/introductiontoqu0000pesk/page/125}}</ref><math display="block"> \alpha = \frac{e^2}{4 \pi} .</math>As such, the fine-structure constant is chiefly a quantity determining (or determined by) the [[elementary charge]]: {{math|1=''e'' = {{sqrt|4''πα''}} ≈ {{val|0.30282212}}}} in terms of such a natural unit of charge.

In the system of [[atomic units]], which sets {{math|1=''e'' = ''ħ'' = 4''πε''{{sub|0}} = 1}}, the expression for the fine-structure constant becomes
<math display="block">\alpha = \frac{1}{c} .</math>