Does the Klein-Gordon Lagrange Density Determine the Solution of the Equation?

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The discussion centers on whether the Klein-Gordon Lagrange density maximizes or minimizes the solution of the Klein-Gordon equation. Clarification is sought regarding the relationship between the solution of the equation and the action. It is noted that the inquiry pertains to the maximization or minimization of the Klein-Gordon action rather than the equation itself. To address this, one must analyze the second functional derivative of the action concerning the fields. Understanding this relationship is crucial for interpreting the implications of the Klein-Gordon Lagrange density.
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Does the Klein-Gordon Lagrange density maximize or minimise the solution of the Klein-Gordon equation?
 
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jimmy.neutron said:
Does the Klein-Gordon Lagrange density maximize or minimise the solution of the Klein-Gordon equation?

This doesn't make sense. Are you asking whether the solution of the Klein-Gordon equation maximizes or minimizes the Klein-Gordon action?
 
Ah yes that's what I meant to ask, I have a foreign lecturer and he's not always that clear with his questions.

Thanks
 
Then if that's what you want to know you have to examine the 2nd (functional) derivative of the action with respect to the fields.
 

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