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Group quantization of the affine field model for gravity and non-standard representations of the SU(1, 1)-Kac-Moody group

The authors quantize the affine field model for gravity on the basis of a group approach. The starting point involves the group C( Sigma , SU(1, 1)) which contains the kinematic affine subgroup that preserves the signature of the metric as well as the subgroup generated by the Hamiltonian density. They work out the quantum wavefunctionals in both coherent state and metric diagonal/energy representations. They show that they provide (exceptional) irreducible representations of C( Sigma , SU(1, 1)) that generalize the exceptional representations of the SU(1, 1) Kac-Moody group with zero central charge.