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1. What is the mathematical formalism where one can transform between field and geometry or they both being emergence?

2. What is the mathematical formalism that can describe QFT but not using the concept of fields nor particles. What are they called and current attempts at this? For example. In Faraday times, Electric fields are flux lines. Then in QM, Electric Fields became potentials. In QFT, Electric Fields became exchange of virtual photons. Is there another formalism where electric fields were described as another dynamics? One closer to perhaps the language of GR? How is the programme progressing if there was one?