I am reading Peskin and Schroeder Section 11.4. They derive a formula for the effective action p.372 Equation 11.63 using a scalar field interaction,

$$ \Gamma \left ( \phi _{cl} \right )=\int d^{4}L_{1}\left [ \phi _{cl} \right ]+\frac{i}{2}\log\text{Det}\left [ \frac{\partial ^{2}L_{1}}{\partial \phi \partial \phi } \right ]$$ $$- i\: Connected\: Diagrams+\int d^{4}x\delta L\left [ \phi _{cl} \right ].\tag{11.63} $$

They use this formula to determine the effective potential. If I want to do the same for a Lagrangian with with a scalar field and fermion field, can I use the same reasoning and technique to get a formula for a scalar field and fermion field?


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