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1

It turns out this diagram (one of eight) was given as an assignment in which we were to uncover the subtleties for ourselves. Considering the free quark propagator in isolation and then looking at the $1$PI correction associated with the gluonic correction (the self energy) , we see that this vanishes in dimensional regularisation with the result that the ...

4

The Einstein field equations $$R_{\mu\nu}~-~\frac{1}{2}Rg_{\mu\nu}~=~8\pi GT_{\mu\nu}$$ for zero stress energy means that the Ricci Curvature $R_{\mu\nu}$ is proportional to the metric with $R_{\mu\nu}~=~\frac{1}{2}Rg_{\mu\nu}$. This is called an Einstein spacetime, and for a constant Ricci scalar $R~=~R_{\mu\nu}g^{\mu\nu}$ this is a spacetime of constant ...

4

You can easily see this isn't the case by considering the special case of the stress-energy tensor equal to zero i.e. the vacuum solutions. These include the Minkowski metric, which is flat, but also the Schwarzschild and Kerr metrics and of course gravitational waves.

2

You are halfway correct. The trace of a combination of $\gamma$-matrices does not depend on the representation in which they are expressed. Sakurai primarily uses the Dirac-Pauli representation, while Peskin and Schroeder use the Weyl chiral representation. This difference in representation should no affect the traces of matrix combinations; the traces ...

0

This link show a lots of properties : https://en.wikipedia.org/wiki/Gamma_matrices Be careful, I think you forgot a minus sign in one of your equation (-2p if I'm not mistaken) But I'm not sure here about the indices of p1 and p2 with the Feynman slash. Can you explicitly gives the indices for those gamma matrices ? I hope the trace identities might help ...

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