Hamiltonian analysis of spin-2 fields with derivative interaction

The Hamiltonian analysis of spin-2 fields including those with derivativeinteractions is performed, starting with explicit analysis of the well known Einstein-Hilbert action . In Hassan-Rosen bimetric theory, a second met-ric is introduced, which has been shown to introduce a second spin two field in addition to the one in general relativity. The kinetic part of the action corresponding to this theory consists of two copies of the Einstein-Hilbert action. The potential part couples the metrics to each other in this theory. One can construct other actions in bimetric theory, with kinetic parts dif-ferent from the Einstein-Hilbert action. These terms will create derivative interactions in the kinetic parts.In this thesis the Hamiltonian analysis of these terms are presentedin detail. The result is shown to be consistent with previous work andin the limit of general relativity and the minisuperspace approximation.The Hamilton analysis show us that the Boulware-Deser ghost in theoriesincluding these terms can be removed. However there is a propagatingghost in these theories since we get a relative sign in the kinetic terms.