Quasi local energy from loop quantum gravity boundary modes

Tuesday, Oct 22

Wolfgang Wieland, Perimeter Institute
Title: Quasi-local energy from LQG boundary modes
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By Jorge Pullin

In physical theories situations can be broken up into subsystems that one can follow individually characterized by a finite number of variables.

However, for nonlinear theories like general relativity one does not necessarily know how to do that. This is related to several problems in the theory like the averaging problem in cosmology. In the latter one typically concentrates on a small number of degrees of freedom of the universe, like its scale, and writes equations for them, pretending the universe is homogeneous, it does not change from one point to the next. This is a coarse approximation, but several important results can be derived from it. The matter content of the universe is not homogeneous and therefore to treat it one typically considers an average. But the average of non-linear functions of some variables is not the same as evaluating those quantities with the average values of the variables. This is known as the averaging problem in cosmology.

In this talk it was proposed to build degrees of freedom for subsystems in general relativity by constructing the degrees of freedom of the whole system starting from those of subsystems. The construction was discussed first in the context of classical general relativity. In the last part of the talk a connection with loop quantum gravity was presented. When one considers subregions of space time in loop quantum gravity the loops pierce the boundaries of the subregions and constitute field theories of "punctures" on them. These naturally embody the degrees of freedom of the subregion. A connection with a particular formulation of loop quantum gravity known as the spinor formulation was also suggested.