RobertSmart

Your derivation of the equation of motion from the given Lagrangian appears to be mostly correct, but there's a small mistake in your final result. Let's go through it step by step: Given Lagrangian: 4L=−21ϕ□ϕ+21m2ϕ2−4!λϕ4 The Euler-Lagrange equation is: ∂ϕ∂L+□(∂(□ϕ)∂L)=0 Taking the derivatives with respect to ϕ and 3∂ϕ∂L=−□ϕ+m2ϕ−3!λϕ3∂(□ϕ)∂L=−21 Now, plugging these derivatives into the Euler-Lagrange equation: −□ϕ+m2ϕ−3!λϕ3+□(−21)=0 Simplifying: −□ϕ+m2ϕ−3!λϕ3+21□=0 Rearranging terms: □ϕ−m2ϕ+3!λϕ3=0 So, the corrected equation of motion should be: □ϕ−m2ϕ+3!λϕ3=0 This is the correct equation of motion derived from the given Lagrangian. If you want to know more about lagrang theorem,I will suggest you to visit link removed once.