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Mar 5, 2020 at 20:34 comment added fewfew4 I wrote the explicit form of the two point function I mentioned in my question. It doesn't have the term I said but it has a different term which isn't I singlet.
Mar 5, 2020 at 13:38 comment added Adam @LucashWindowWasher It doesn't have to, it can also involve the metric $\eta_{\mu\nu}$.
Mar 4, 2020 at 21:34 comment added fewfew4 You can't say the same thing for space-time indices though. Consider the two point function between field strengths $\langle F_{\mu\nu}(x)F_{\rho\sigma}(y)\rangle$. The result involves a term with $(x-y)_{\mu}(x-y)_{\nu}(x-y)_{\rho}(x-y)_{\sigma}$. Does this imply that Lorentz symmetry is spontaneously broken?
Mar 4, 2020 at 21:20 history answered Adam CC BY-SA 4.0