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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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closed as too localized by David Z Dec 1 '11 at 15:26

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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