Editing Action (physics) (section)

=== Single relativistic particle ===
{{Main|Relativistic Lagrangian mechanics|Theory of relativity}}

When relativistic effects are significant, the action of a point particle of mass ''m'' travelling a [[world line]] ''C'' parametrized by the [[proper time]] <math>\tau</math> is
<math display="block">S = - m c^2 \int_{C} \, d \tau. </math>

If instead, the particle is parametrized by the coordinate time ''t'' of the particle and the coordinate time ranges from ''t''<sub>1</sub> to ''t''<sub>2</sub>, then the action becomes
<math display="block">S = \int_{t1}^{t2} L \, dt,</math>
where the [[Lagrangian mechanics|Lagrangian]] is<ref>L. D. Landau and E. M. Lifshitz (1971). ''The Classical Theory of Fields''. Addison-Wesley. Sec.&nbsp;8. p.&nbsp;24–25.</ref>
<math display="block">L = -mc^2 \sqrt{1 - \frac{v^2}{c^2}}.</math>