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CATEGORIES:Mathematical Physics Seminar
SUMMARY: Quantum geometry from the quantisation of gravita
tional boundary modes on a null surface - Wolfgang
Wieland (Perimeter)
DTSTART;TZID=Europe/London:20180501T160000
DTEND;TZID=Europe/London:20180501T170000
UID:TALK100873AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/100873
DESCRIPTION:It is arguably one of the main achievements of loo
p quantum\ngravity to have demonstrated that space
itself may have an atomic structure.\nOne of the
key open problems of the theory is to reconcile th
e discrete\nspectra of geometric observables (such
as area and volume) with general\nrelativity in t
he continuum. In this talk\, I present recent prog
ress\nregarding this issue: I will show that the l
oop gravity discreteness of\nspace can be understo
od from a conventional Fock quantisation of\ngravi
tational boundary modes on a null surface. These b
oundary modes are\nfound by considering a quasi-lo
cal Hamiltonian analysis\, where\ngeneral relativi
ty is treated as a Hamiltonian system in domains w
ith inner\nnull boundaries. The presence of such n
ull boundaries requires then an\nadditional bounda
ry term in the action. Using Ashtekar’s original S
L(2\,C)\nself-dual variables\, I will explain that
the natural such boundary term is\nnothing but a
kinetic term for a spinor (defining the null flag
of the\nboundary) and a spinor-valued two-form\, w
hich are both intrinsic to the\nboundary. Finally\
, we will turn to the quantum theory and I will ex
plain how\nthe cross-sectional area two-form on th
e null surface turns into the\ndifference of two n
umber operators. The resulting area spectrum is di
screte.\nSpin networks or triangulations of space
do not enter the construction.\n
LOCATION:MR11
CONTACT:Professor Maciej Dunajski
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