I feel like this question has been asked before but I can't find it. would the Euler Lagrange equation for, say, the standard model Lagrangian be ∂L∂ϕ=∂μ∂L∂(∂μϕ)
Where ϕ is whatever field is an question and μ is (I believe) being summed from 0 to 3. Or, ist the correct equation ∂L∂ϕ=Dμ∂L∂(Dμϕ)
Where D is the covariant derivative of the theory. My intuition tells me its the second eqn but i just wanted to be sure, and I think I once saw someone say that the two were equivalent.
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