  Of the contributions to the cosmological constant, zero-point energy and self
energy contributions scale as $\Lambda^4$ where $\Lambda$ is an ultraviolet
cutoff used to regulate the calculations. I show that such contributions vanish
when calculated in perturbation theory. This demonstration uses a little-known
modification to perturbation theory found by Honerkamp and Meetz and by
Gerstein, Jackiw, Lee and Weinberg which comes into play when using cutoffs and
interactions with multiple derivatives, as found in chiral theories and
gravity. In a path integral treatment, the new interaction arises from the path
integral measure. This reduces the sensitivity of the cosmological constant to
the high energy cutoff significantly, although it does not resolve the
cosmological constant problem. The feature removes one of the common
motivations for supersymmetry. It also calls into question some of the results
of the Asymptotic Safety program. Covariance and quadratic cutoff dependence
are also briefly discussed.
