We reconsider perturbative unitarity in quantum field theory and upgrade
several arguments and results. The minimum assumptions that lead to the largest
time equation, the cutting equations and the unitarity equation are identified.
Using this knowledge and a special gauge, we give a new, simpler proof of
perturbative unitarity in gauge theories and generalize it to quantum gravity,
in four and higher dimensions. The special gauge interpolates between the
Feynman gauge and the Coulomb gauge without double poles. When the Coulomb
limit is approached, the unphysical particles drop out of the cuts and the
cutting equations are consistently projected onto the physical subspace. The
proof does not extend to nonlocal quantum field theories of gauge fields and
gravity, whose unitarity remains uncertain.Comment: 37 pages, 9 figures; v2: minor changes, Phys. Rev.
