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Would you dig a ditch with a surgeons scalpel? Yes, quantum mechanics ultimately underlies all physical observations but the mathematical expressions for large dimensions with respect to $\hbar$ become cumbersome and are replaced by the simplest ones for the appropriate study. Thermodynamics, for the study of bulk matter, blends smoothly with quantum ...


2

As to your question, yes, the QED Lagrangian is indeed invariant under charge conjugation. You may have found differently because your transformations under charge conjugation are faulty. The prefactors are correct, however, under charge conjugation $\psi$ goes to $\bar{\psi}$ and vice versa, i.e. $$ \hat{C} \, \psi \, \hat{C} = -i(\bar\psi \gamma^0 ...


1

Your statement that the integral "is actually" $\propto g^{\mu\nu}\Pi$ is incorrect because you can clearly see the $q^\mu q^\nu$ in the numerator of the integrand. The correct expression that you have in your final equation is not a choice, it is the result of calculating the loop using dimensional regularization. Finally, indeed $q_\mu \Pi_2^{\mu\nu}$ is ...



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