Euler–Lagrange equation Lagrangian field
where 





L




{\displaystyle {\mathcal {L}}}

 is the Lagrangian density, 






ϕ
˙





{\displaystyle {\dot {\phi }}}

 is the time-derivative of the field, ∇ is the gradient operator, and m is a real parameter (the "mass" of the field). Applying the Euler–Lagrange equation on the Lagrangian:
