Barak Shoshany, Perimeter Institute
Title: 2+1D loop quantum gravity on the edge
PDF of the talk (9M)
Audio+Slidesof the talk (32M)
A technique for studying quantum field theories that has been very successfully applied to the Yang-Mills theories of particle physics is discretization. In it, one replaces the differential equations for the theory for equations in finite differences. Among other things, this makes them amenable to treat them using computers.
A problem that arises when trying to apply these techniques in gravity is that the discretization tends to clash with the symmetries of the theory. In theories of gravity of geometric type, like general relativity, points in space-time can be smoothly moved around, a symmetry known as diffeomorphisms. The rigid nature of discretization breaks that symmetry.
This talk addresses this problem through a technique known as coarse graining. In it, one breaks physical systems into subsystems and characterizes the latter through observable quantities that are invariant under the symmetries of the theory. This leads to observables associated with the edges of the region, hence the title of the talk. The coarse graining allows to introduce discretizations compatible with the symmetries of general relativity. This is shown in detail in this talk for the 2+1 dimensional case.
One of the features found is that when piecing together the domains of the coarse graining, the edge degrees of freedom cancel out and one is left only with corner degrees of freedom that can be thought as "particle excitations". The space of quantum states is that of ordinary loop quantum gravity (spin networks) with the addition of the particle excitations. The work shows that spin networks can be obtained by classically discretizing general relativity. This opens possibilities for studying the classical limit and the dynamics. Work is in progress to generalize the results to 3+1 dimensions.
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