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Null Twisted Geometry

Dec 04
Group Seminar
4:30 pm o'clock to 5:30 pm o'clock
Mingyi Zhang
SR 02.729

The talk presents the quantization of null hypersurfaces in the context of loop quantum gravity (LQG). We use the twistorial parametrisation of LQG, and fix the normal in the linear simplicity constraints to be null.The main discovery is that the simplicity constraints in this formalism are all first class, and the symplectic reduction selects only the helicity subgroup of the little group ISO(2). It can be described by an Euclidean singular structure on the 2-dimensional space-like surface. The quantization of this system ends up with the spin-networks labelled by SO(2) quantum numbers, embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group. Finally I will give some possible applications and research directions based on our work.