Hamiltonian BRST-invariant deformations in Abelian gauge theory with higher derivative matter fields

We construct the consistent interactions among the Abelian gauge fields and various higher derivative matter fields within the framework of the Hamiltonian BRST formalism. To achieve this, we mainly investigate a set of iterative equations with respect to the free model under study by using the cohomological technique. Concretely, it is shown that the second-order and the other higher-order deformations of the BRST charge are supposed to be zero. While for the BRST-invariant Hamiltonian, the third-order as well as the corresponding higher-order deformation terms vanish completely for scalar fields. In special, the deformation of BRST-invariant Hamiltonian for the spinor field model terminates at order one as we can imagine. Furthermore, after plugging these deformed quantities into the original Hamiltonian and exploiting the ghost-independent terms, we recover the usual local gauge symmetries of the resulting interacting theory which can be interpreted as the gaugings of the rigid invariance of the uncoupled system.