Restoring S.I. units to a Lagrangian in natural units

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SUMMARY

The discussion focuses on the process of restoring S.I. units to a Lagrangian originally expressed in natural units. It concludes that to achieve this restoration, one must incorporate specific scaling factors that correspond to the field in question, rather than merely reintroducing the fundamental quantities that were initially omitted. The key takeaway is that only quantities relating to different dimensions are excluded in the formulation of natural units, not the fundamental quantities themselves.

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  • Understanding of Lagrangian mechanics
  • Familiarity with natural units in physics
  • Knowledge of dimensional analysis
  • Basic concepts of field theory
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Precious Adegbite
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TL;DR
Restoring the Lagrangian units
If we have a natural unit Lagrangian, where some fundamental quantities have been excluded to ease calculations...and aim to restore it's S.I units back, do we just have to plug back the fundamental quantities that were initially excluded Into the Lagrangian...or we use some specific scaling factors corresponding to that field that has the same S.I units of Lagrangian density, and scale the unitless Lagrangian with it.
 
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"fundamental quantities" are not excluded in using natural units.
Only quantities relating two different dimensions are excluded.
 

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