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This is a study of Non-Local Gauge Invariant Quantum Field Theory. NonLocal gauge invariance is an extension of the group of local gauge transformations that has been extensively used in construction of physical theories. We show how this larger group is rich enough to accommodate a new theory of gravity, and we propose a new model of uni cation of gravitational and electromagnetic interactions. This new model of gravity has the advantage over the general relativity of being a quantizable theory."