In sense of classical mechanics+special relativity what is lagrangian of a photon? Lagrangian of a relativistic massive particle is as follows: $$ L_{massive}= -mc\sqrt{c^2-v^2} $$ So is it a zero?
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Classical electrodynamics has a lagrangian for the classical fields, see discussion here .
The photon is an elementary particle and does not have a classical existence.
Here is on page 5 the Lagrangian for a photon
