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New boundary variables for classical and quantum gravity on a null surface

Nov 21
Group Seminar
2:00 pm o'clock to 4:00 pm o'clock
Dr. Wolfgang Wieland (Perimeter Institute for Theoretical Physics)
SR 02.729

In my talk, I introduce new canonical boundary variables for classical and quantum gravity on a null surface. At the classical level, general relativity will be considered as a Hamiltonian system in domains with inner null boundaries. The presence of such lightlike boundaries requires then additional boundary terms in the action. Using Ashtekar’s original SL(2,C) selfdual variables, I will explain that the natural such boundary term is nothing but a kinetic term for a spinor (defining the null flag of the boundary) and a spinor-valued two-form, which are both intrinsic to the boundary. Finally, the relevance of this new boundary term for the definition of quasi-local observables and for quantum gravity in particular will be explained. In fact, the oriented area of a two-dimensional cross section of the null boundary turns into the difference of two number operators. The resulting area spectrum is discrete and agrees with the results from loop quantum gravity. The entire derivation happens at the level of the continuum theory, and no spin-networks or SU(2) gauge variables are ever required for deriving this result.