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SUMMARY: Quantum geometry from the quantisation of gravitational boundary
  modes on a null surface - Wolfgang Wieland (Perimeter)
DTSTART:20180501T150000Z
DTEND:20180501T160000Z
UID:TALK100873@talks.cam.ac.uk
CONTACT:Professor Maciej Dunajski
DESCRIPTION:It is arguably one of the main achievements of loop quantum\ng
 ravity to have demonstrated that space itself may have an atomic structure
 .\nOne of the key open problems of the theory is to reconcile the discrete
 \nspectra of geometric observables (such as area and volume) with general\
 nrelativity in the continuum. In this talk\, I present recent progress\nre
 garding this issue: I will show that the loop gravity discreteness of\nspa
 ce can be understood from a conventional Fock quantisation of\ngravitation
 al boundary modes on a null surface. These boundary modes are\nfound by co
 nsidering a quasi-local Hamiltonian analysis\, where\ngeneral relativity 
 is treated as a Hamiltonian system in domains with inner\nnull boundaries
 . The presence of such null boundaries requires then an\nadditional bounda
 ry term in the action. Using Ashtekar’s original SL(2\,C)\nself-dual var
 iables\, I will explain that the natural such boundary term is\nnothing bu
 t a kinetic term for a spinor (defining the null flag of the\nboundary) an
 d a spinor-valued two-form\, which are both intrinsic to the\nboundary. Fi
 nally\, we will turn to the quantum theory and I will explain how\nthe cro
 ss-sectional area two-form on the null surface turns into the\ndifference 
 of two number operators. The resulting area spectrum is discrete.\nSpin ne
 tworks or triangulations of space do not enter the construction.\n
LOCATION:MR11
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