  A perturbative renormalization group is formulated for the study of
Hamiltonian light-front field theory near a critical Gaussian fixed point. The
only light-front renormalization group transformations found that can be
approximated by dropping irrelevant operators and using perturbation theory
near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs
violate covariance and cluster decomposition, and allow functions of
longitudinal momenta to appear in all relevant, marginal, and irrelevant
operators. These functions can be determined by insisting that the Hamiltonian
display a coupling constant coherence, with the number of couplings that
explicitly run with the cutoff scale being limited and all other couplings
depending on this scale only through perturbative dependence on the running
couplings. Examples are given that show how coupling coherence restores Lorentz
covariance and cluster decomposition, as recently speculated by Wilson and the
author. The ultimate goal of this work is a practical Lorentz metric version of
the renormalization group, and practical renormalization techniques for
light-front quantum chromodynamics.
