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- Wolfgang Wieland

Senior Postdoctoral Fellow

Area of Research:

Phone: (519) 569-7600 x7526

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 excite a surface charge, namely a spinor (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. In the last couple of papers, I develop the Hamiltonian formalism for these null boundary spinors. The next step is to compute the algebra of observables and understand the dynamics in terms of these variables at the level of the quantum theory.

- 2013--2015, Postdoctoral scholar at the Institute for Gravitation and the Cosmos (Pennsylvania State University, United States)

- E. Adjei, S. Gielen, W. Wieland, Cosmological evolution as squeezing: a toy model for group field cosmology,

Class. Quantum Grav. 35 (2018), 105016, arXiv: 1712.07266. - W. Wieland, Quantum gravity in three dimensions, Witten spinors and the quantisation of length,

Nuclear Physics B 930 (2018), 219-234, arXiv: 1711.01276. - W. Wieland, New boundary variables for classical and quantum gravity on a null surface,

Class. Quantum Grav. 34 (2017), 215008 (30pp), arXiv: 1704.07391. - W. Wieland, Fock Representation of Gravitational Boundary Modes and the Discreteness of the Area Spectrum,

Ann. Henri Poincaré 18 (2017), 3695, arXiv: 1706.00479. - 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 Poincaré 12 (2012), 425, arXiv: 1012.1738. - W. Wieland, Loop quantum gravity and the continuum, arXiv: 1804.08643.
- 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.

- APS April Meeting 2018 (Columbus, Ohio),
Loop Quantum Gravity and the Quantization of Null Surfaces , 2017-07-05,slides . - Loops'17 (Warsaw, Poland),
New boundary variables for classical and quantum gravity , 2017-07-05,slides . New boundary variables for CQG on a null surface , Seminar given at IQOQI (Vienna, Austria), 2017-07-25.Spinors as boundary variables for gravity on a null surface , Seminar given at the Gravitational Physics Group at the University of Vienna, 2017-03-01.- Fifth Tux winter workshop on Quantum Gravity (Tux, Austria),
Spinors as boundary variables for gravity on a null surface , 2017-02-21. Spinors as boundary variables for gravity on a null surface , Seminar given at the Centre de Physique Théorique (Marseille, France), 2017-02-21.Four Lectures on non-perturbative quantum gravity , Lectures held at the Institute for Theoretical Physics at the University of Innsbruck, February 2017.Discrete Gravity as a topological field theory with defects , Seminar given at Louisiana State University (Baton Rouge, USA), November 2016.Quasilocal free energy: Positivity and monotonicity , Seminar given at Caltech, October 2016.

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