Fine-structure constant: Difference between revisions

Revision as of 17:58, 19 December 2024

Revision as of 16:56, 10 January 2025

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<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 expressionsexpression 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.

<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'' = ''m''{{sub|e}} = ''ħ'' = 4''πε''{{sub|0}} = 1}}, the expression for the fine-structure constant becomes