We present a nonperturbative quantization of gravitational null initial data. Our starting point is the characteristic null initial problem for tetradic gravity with a parity-odd Holst term in the bulk. After a basic review about the resulting Carrollian boundary field theory, we introduce a specific class of impulsive radiative data. This class is defined for a certain choice of relational clock. With respect to this clock, the shear of the null congruence that generates the boundary follows the profile of a step function. The angular dependence is arbitrary. Next, we solve the residual constraints, which are the Raychaudhuri equation and a Carrollian transport equation for an $SL(2,\mathbb{R})$ holonomy. We show that the resulting submanifold in phase space is symplectic. Along each null generator, we end up with a simple mechanical system. The quantization of this system is straightforward. Our basic strategy is to start from an auxiliary Hilbert space with constraints. The physical Hilbert space is the kernel of a constraint, which is a combination of ladder operators. The constraint and its Hermitian conjugate are second-class. Solving the constraint amounts to imposing a simple recurrence relation for physical states. On the resulting physical Hilbert space, the $SL(2,\mathbb{R})$ Casimir is a Dirac observable. This observable determines the spectrum of the two radiative modes. Another class of Dirac observables is given by the cross-sectional area densities at the initial and final cuts of the null surface. The resulting area spectrum is discrete, which agrees with earlier results on this topic.

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• Canonical quantum gravity
• General relativity
• Gravitational waves
• Loop quantum gravity
• Quantum gravity