I am not as well read as most of the people in here so I thought I would ask you guys first. What work has been done in the way of developing a covariant field theory? I'm going to ramble for just a little bit so try to follow. It seems to me that QFT is built on two principles Poincare invariance and the Structure Decomposition Principle. A covariant field theory, in my opinion, would be built on basically the same two things except this time it would be General covariance and the Structure Decomposition Principle. The structure decomposition principle implies, in my mind, the need for creation and annihilation operators, and the covariant part would require the generalization of the concept of a field. I am referring to this generalization as a covariant field. The homogeneous Lorentz group is O(3,1) and the corresponding generally covariant homogeneous group, at least locally, is GL(R,4). I guess my question is: is GL(R,4) unitarizable? Have people come up with the concept of a covariant field? If they have, why did it not work? Is it non-renormalizable, power counting sense? The reason I ask is because I think I have a covariant field theory. It's not completely done yet.