Wolfgang Wieland: Quantum Geometry of the Light Cone

mardi 12 mars 2024, 10:30 → 11:30 Europe/Paris

Recently, I introduced a non-perturbative quantization of 
impulsive gravitational null initial data. In this talk, I present the 
key results established thus far. The 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, I will introduce a specific 
class of impulsive radiative data. This class is defined for a specific 
choice of relational clock. The clock is chosen in such a way that the 
shear of the null boundary follows the profile of a step function. The 
angular dependence is arbitrary. Next, I explain how to solve the 
residual constraints, which are the Raychaudhuri equation and a 
Carrollian transport equation for an SL(2,R) holonomy. 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. The physical Hilbert space is the kernel of a 
constraint, which is a combination of ladder operators. Solving the 
constraint amounts to imposing a simple recurrence relation for physical 
states. One of the quantum numbers is the total luminosity carried to 
infinity. I show that a transition happens when the luminosity reaches 
the Planck power. Below the Planck power, the spectrum of the radiated 
power is discrete. Above the Planck power, the spectrum is continuous 
and contains caustics that can be avoided only when the spectrum is 
discrete.