PIRSA:12020129

Spinor Quantisation for Complex Ashtekar Variables

Wieland, W. (2012). Spinor Quantisation for Complex Ashtekar Variables. Perimeter Institute. https://pirsa.org/12020129

Wieland, Wolfgang. Spinor Quantisation for Complex Ashtekar Variables. Perimeter Institute, Feb. 29, 2012, https://pirsa.org/12020129 

          @misc{ pirsa_PIRSA:12020129,
            doi = {10.48660/12020129},
            url = {https://pirsa.org/12020129},
            author = {Wieland, Wolfgang},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Spinor Quantisation for Complex Ashtekar Variables},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {feb},
            note = {PIRSA:12020129 see, \url{https://pirsa.org}}
          }

Wolfgang Wieland

University of Erlangen-Nuremberg

Talk number
PIRSA:12020129
Collection
Talk Type
Subject
Abstract
During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll scatch my current project concerning a twistorial path integral for spinfoam gravity as well.