An introduction to covariant loop quantum gravity
Wednesday, 24 Feb. 2016, 15:30 - 17:00
Presenter: Wolfgang Wieland
Host: Philipp Höhn
Where: IQOQI Seminar Room, 2nd Floor, Boltzmanngasse 3, 1090 Vienna
Quantum theory has taught us that nature is intrinsically probabilistic. The lesson from general relativity, on the other hand, is that gravity is not merely another field in Minkowski space, gravity gives spacetime its very shape and geometry. If gravity is to be quantised, the minute structure of space and time — indeed geometry itself — should therefore be quantised. Loop quantum gravity is a concrete realisation of this idea. My talk gives an introduction to the theory, and presents recent developments in the field. I sketch the construction of the Hilbert space of the theory, which is based on Ashtekar’s reformulation of general relativity in terms of SU(2) Yang—Mills variables. The quantum states of geometry live on the boundary of spacetime and can be expanded in terms of Penrose’s spin-network functions, which form an orthonormal basis. Areas, angles and volumes turn into self-adjoint operators with discrete spectra. The dynamics of general relativity is regained at the quantum level by solving the Wheeler—DeWitt equation. A concrete proposal for the construction of its solutions is given in terms of spin-foam amplitudes, which represent the evolution of spin-network functions in time.