New Methods in Quantum Non-Local Field Theory

Functional methods are developed which serve to simplify greatly the calculations in quantum non-local field theory (QNFT). The techniques also serve to give an insight into the underlying structure of QNFT. We show that a transformation can be defined which relates the QNFT Lagrangian to its local antecedent. We prove that the non-local extension of the local gauge symmetry can be obtained by applying this transformation to the local gauge transformation. The utility of this method is demonstrated by an explicit application to both scalar electrodynamics and Yang-Mills field theory.