Introduction to Nonlocal Field Theory Including Gravity

We give minireview of nonlocal field theory (infinite derivative field theory). We start with the discussion of the main peculiarities of nonlocal field theory on the example of \(d = 4\) scalar \({{\phi }^{4}}\)-model. The nonlocal \({{\phi }^{4}}\)-model is ultraviolet finite, unitary, and macrocausal. One of the problems of nonlocal field theory is that the formfactor is an arbitrary entire function that makes the predictions extremely weak. We propose some additional principle that allows to fix the formfactor. Also we review the main results obtained in nonlocal quantum gravity, namely the nonlocal generalization of Einstein gravity leads to the superrenormalizable theory.