Quantum, Local, and Background Free

I’ve just finished reading a great general conference proceeding by John Baez on Topological Quantum Field Theory (TQFT, my thanks to Kevin for pointing it out). While the details of TQFT were easy to understand and interesting, the most compelling thing to me was his exposition on what a theory of quantum gravity should look like, i.e., that it be a “… background-free quantum theory with local degrees of freedom propagating causally.” I’m sure that I’ve heard it said in this way before, but for some reason this crystalized in my mind the real program that we are undertaking… its sounds so easy, doesn’t it!

I’m still working my way through QFT, and I’ve not yet encountered attempts to combine QFT with GR. If someone asked me, in all my naivete, to combine these two, I would take the entire Standard Model Lagrangian and replace the Minkowski metric with the dynamic GR metric, \eta_{\mu\nu}\rightarrow g_{\mu\nu}, and add a term for the Lagrangian density of the Einstein-Hilbert action. Of course, I’m ignoring the fact that we need to quantize the field g_{\mu\nu}, which I imagine is where the difficulty resides. My question is, where can I find a good description of where this prescription breaks down?

As always, you can come visit me here!

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