  Neutrices are additive groups of negligible functions that do not contain any
constants except 0. Their calculus was developed by van der Corput and Hadamard
in connection with asymptotic series and divergent integrals. We apply neutrix
calculus to quantum field theory, obtaining finite renormalizations in the loop
calculations. For renormalizable quantum field theories, we recover all the
usual physically observable results. One possible advantage of the neutrix
framework is that effective field theories can be accommodated. Quantum gravity
theories appear to be more manageable.
