Show that the Lorentz invariant Lagrangian (in the sense of Section 12.1B) L = mU
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Show that the Lorentz invariant Lagrangian (in the sense of Section 12.1B)
L = – mUαUα/2 – q/c UαAα
gives the correct relativistic equations of motion for a particle of mass m and charge q interacting with an external field described by the 4-vector potential Aα(x).
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