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In classical Hamiltonian mechanics one has the generalized coordinates $q^{i}(t)$ and momenta $p_{i}(t)$. The Poisson bracket is defined as, $$[F,G]_{PB}=\frac{\partial F}{\partial q^{k}}\frac{\partial G}{\partial p_{k}}-\frac{\partial F}{\partial p_{k}}\frac{\partial G}{\partial q^{k}}\ .$$ Using the q's and p's in place of $F$ and $G$ one has the ...
Suppose $A$ is at the space-time origin $0$, and $B$ is at space-time event $x$. You suppose that a real photon could go from $A$ to $B$, so this means that $A$ and $B$ are separated by a light-like interval, that is $x^2 = (x^0)^2- \vec x^2=0$. This means that $x^0>0$, too. Now, the propagator $D_{\mu\nu}(x)$ represents the amplitude for a photonic ...