Since gravity is so similar with the Yang-Mills theory, the Christoffel connection is the gauge potential, the Riemann curvature is the field strength, then why is quantising gravity so difficult when we already have a successful quantum yang-mills theory? I know by dimensional analysis, we can deduce that Einstein theory is not renormalizable. But are there something else truly essential that make quantising gravity so difficult?
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You said it already. Effective quantization of gravity is being used in the cosmological model during the inflation period, pushing under the rug non renormazibility. String theories have quantized gravity, no problems of infinities there, but there is no one string model from the thousands of possibilities. Patience for research to come up with one. – anna v Mar 19 '16 at 11:20
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3It's not perturbatively renormalizable. Also, duplicate of A list of inconveniences between quantum mechanics and (general) relativity? – ACuriousMind Mar 19 '16 at 11:28