= Derivation of the Dirac equation
The <Dirac equation> can be derived basically "directly" from the <Representation theory of the Lorentz group> for the <spin half> representation, this is shown for example at <Physics from Symmetry by Jakob Schwichtenberg (2015)> 6.3 "Dirac Equation".
The Diract equation is the <spacetime symmetry> part of the <quantum electrodynamics Lagrangian>, i.e. is describes how <spin half> particles behave without interactions. The full <quantum electrodynamics Lagrangian> can then be reached by adding the <U(1)> <internal symmetry>.
As mentioned at <spin comes naturally when adding relativity to quantum mechanics>, this same method allows us to analogously derive the equations for other <spin numbers>.
Bibliography:
* <video Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)> at https://youtu.be/OCuaBmAzqek?t=743
* https://www.youtube.com/watch?v=zM-Lc16nyho&list=PL54DF0652B30D99A4&index=66 "L3. The Dirac Equation" by doctorphys
* <video Dirac equation for the electron and hydrogen Hamiltonian by Barton Zwiebach (2019)>
\Video[https://www.youtube.com/watch?v=jjG2Y_dMsbI]
{title=Deriving The <Dirac equation> by <Andrew Dotson> (2019)}