Talks by Wolfgang Wieland

Null infinity from quasi-local phase space

I will consider the phase space at null-infinity from the r\rightarrow\infty limit of a quasi-local phase space for a finite box with a boundary that is null. This box will serve as a natural IR regulator. To remove the IR regulator, I will consider a double null foliation together with an adapted Newman--Penrose null tetrad. The limit to null infinity (on phase space) is obtained in the limit where the boundary is sent to infinity. I will introduce various charges and explain the role of the corresponding balance laws. The talk is based on the paper: arXiv:2012.01889.

 

Worldline formalism for covariant loop gravity

I present a proposal for a worldline action for discretized gravity with the same field content as loop quantum gravity. The proposal is defined through its action, which is a one-dimensional integral over the edges of the discretization. Every edge carries a finite-dimensional phase space, and the evolution equations are generated by a Hamiltonian, which is a sum over the constraints of the theory. I will explain the relevance of the model, and close with possible relations to other approaches of quantum gravity, including: relative locality, causal sets and twistor theory.

A one-dimensional action for simplicial gravity in three dimensions

Loop quantum gravity has a spinorial representation. Spinors simplify the symplectic structure of the theory, but can they also teach us something about the dynamics? We study this question in three dimensions, and derive the Ponzano–-Regge model from a spinorial action. Our construction starts from the first-order Palatini formalism, and gives the discretised action in the spinorial representation. A one-dimensional refinement limit brings us back to a continuum theory. The three-dimensional action turns into a line integral over the edges of the discretisation.

Spinor Quantisation for Complex Ashtekar Variables

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).