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Note: some chapters of Robert Klauber's excellent book are downloadable for free.
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In my intermittent progress through Robert Klauber's excellent "Student Friendly Quantum Field Theory" I'm currently working through the relativistic versions of the Schrödinger equation (prior to hitting QFT-proper).
These are indexed by spin. Schrödinger's non-relativistic equation which is the staple of introductory quantum mechanics courses, works for spin-1/2 fermions like the electron to which it is usually applied.
The most direct relativistic counterpart is Klein-Gordon, which Schrödinger considered first but couldn't make work for the hydrogen atom. This is because it actually applies to spin-0 particles (scalar bosons such as the Higgs particle).
The correct relativistic equation for the electron and other spin-1/2 fermions is named after Dirac, while vector bosons such as the photons (spin 1) have their own Proca equation.
So I was wondering if the spin-2 graviton has its own equation .. but then I recalled that quantum theory can't do gravity yet - see this.
Here's a convenient, semi-impenetrable table.
