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Homework Statement
2N classical, real, scalar fields \phi_i (x^{\nu}) \psi_i (x^{\nu}) ,where i=1,...,N
I have to find the equations of motions for \phi_i (x^{\nu}) \psi_i (x^{\nu})
Lagrange density is given by
L= \sum_{i=1}^N (\frac{1}{2}(\partial_{\mu} \phi_i \partial^{\mu} \phi_i+\partial_{\mu} \psi_i \partial^{\mu} \psi_i-m^2(\phi_i \phi_i + \psi_i \psi_i) - \lambda \phi_i \psi_i))
Homework Equations
Euler-Lagrange equation
\partial_{\mu} \frac{\partial L}{\partial (\partial_{\mu} \phi_i)} - \frac{\partial L_0}{\partial \phi_i} = 0
The Attempt at a Solution
The problem for me is the interaction term? Can I just put in the Euler-Lagrange equation as well, or what do I do with it? I found some equations by disregarding the interaction term
\partial_{\mu} \partial^{\mu} \phi_i + m^2 \phi_i = 0
\partial_{\mu} \partial^{\mu} \psi_i + m^2 \psi_i = 0
Is this right?
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