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in case of fields is called "lagrangian density"

let particle with mass "m" and position "x"

it kientic energy= 1/2(mv^2)

so lagrangian =1/2(mv^2)-v(x) , v(x)=potential energy

in case the field lagrangian density

how can i determine the lagragian density?

for klein gordon eq

dirac eq and any field

please any one help