- Home »
- Wolfgang Wieland

Spinors are fascinating objects at the interplay between quantum theory, information, geometry and general relativity. In quantum theory, they represent the smallest possible quantum systems. In general relativity, they appear as mathematical tools for e.g. Witten's proof of the positive energy theorem, or the geometric analysis of null congruences and asymptotic null infinity. In my own research, I am considering the possibility that quantum gravity is built from such spinors alone. The idea is quite easy to justify: In loop quantum gravity, the quantum states of geometry are built from Wilson lines for a spin connection, and if these Wilson lines hit a two-dimensional boundary they create a surface charge, and this surface charge is nothing but spin (the mechanism is similar to string theory, where the Chan--Patton factors sit at the open ends of strings). In fact, one can show that these loop gravity *boundary spinors* are nothing but the canonical boundary variables for general relativity on a null surface. The goal is to develop this further and understand the dynamics in terms of these boundary spinors as well.

- W. Wieland, Discrete gravity as a topological field theory with light-like curvature defects,

JHEP 5 (2017), 142, arXiv: 1611.02784. - W. Wieland, Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations,

Gen. Rel. Grav. 49 (2017), 38, arXiv: 1604.07428. - W. Wieland, New action for simplicial gravity in four dimensions,

Class. Quant. Grav. 32 (2015), 015016, arXiv: 1407.0025. - W. Wieland, A one-dimensional action for simplicial gravity in three dimensions,

Phys. Rev. D 90 (2014), 044008, arXiv: 1402.6708. - W. Wieland, Hamiltonian spinfoam gravity,

Class. Quant. Grav. 31 (2014), 025002, arXiv: 1301.5859. - E. Bianchi, M. Han, E. Magliaro, C. Perini, C. Rovelli, W. Wieland, Spinfoam fermions,

Class. Quant. Grav. 30 (2013), 235023, arXiv: 1012.4719. - H. M. Haggard, C. Rovelli, F. Vidotto, W. Wieland, The spin connection of twisted geometry,

Phys. Rev. D 87 (2013), 024038, arXiv: 1211.2166. - S. Speziale, W. Wieland, The twistorial structure of loop-gravity transition amplitudes,

Phys. Rev. D. 86 (2012), 124023, arXiv: 1207.6348. - W. Wieland, Twistorial phase space for complex Ashtekar variables,

Class. Quant. Grav. 29 (2012), 045007, arXiv: 1107.5002. - W. Wieland, Complex Ashtekar variables and reality conditions for Holst's action,

Annales Henri PoincarÃ© 12 (2012), 425, arXiv: 1012.1738. - W. Wieland, Fock representation of gravitational boundary modes and the discreteness of the area spectrum, arXiv: 1706.00479.
- W. Wieland, New boundary variables for classical and quantum gravity on a null surface, arXiv: 1704.07391.
- E. Bianchi, W. Wieland, Horizon energy as the boost boundary term in general relativity and loop gravity, arXiv: 1205.5325.
- W. Wieland, Complex Ashtekar variables, the Kodama state and spinfoam gravity, arXiv: 1105.2330.
- W. Wieland, Simplified Hamiltonian constraint for a particular value of the Barbero--Immirzi parameter, arXiv: 0912.3443.

©2012 Perimeter Institute for Theoretical Physics