# Find equations of motion from given Lagrangian density [closed]

Could someone help me solve this probably not very hard problem?

Given Lagrangian Density:

$\mathcal L=\bar{\psi}(i\gamma^\mu\partial_\mu-g\gamma^5\phi)\psi+\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)-\frac{1}{2}m^2\phi^2$

• Find the equations of motion for the wave-functions $\psi$ and $\phi$
• Demanding parity-invariance of the Lagrangian, show how $\phi$ transforms under parity
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Hi vedran, and welcome to Physics Stack Exchange! This is a site for conceptual questions about physics, not for general assistance with homework (or homework-like) problems. If you can edit your question to focus on the specific physical principle which is giving you trouble, rather than just asking how to do the problem, I would be happy to reopen it. –  David Z Dec 1 '11 at 15:33
This problem is not well posed, and this is probably the instructor's fault--- Lagrangians are not of "wavefunctions", they are only of "fields". If some source says that the real field $\phi$ is a wavefunction, this source is not worth learning from. The field $\psi$ is not a real number, but a Grassman variable (even worse). Without knowing these two things, you can do formal manipulations of dubious pedagogical value to get the answer, without understanding anything. –  Ron Maimon Dec 1 '11 at 18:42