A quantization of (2+1)-gravity related to high-energy Yang–Mills theory

We point out that canonical quantization of the two-body problem in (2+1)-gravity is related to the high-energy equation in Yang–Mills theory by a proper ordering of the relevant operators. This feature arises from expanding the Hamiltonian around its conformal limit—or treating running coupling effects in the Yang–Mills case—and yields a peculiar short distance behaviour of the wave functions.