Quantum geometry from higher gauge theory

Tuesday, Sep 10th

Bianca Dittrich, Perimeter Institute
Title: Quantum geometry from higher gauge theory
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By Jorge Pullin, LSU


Physical theories are usually formulated in terms of sets of redundant variables. A simple example would be to consider the position of a pendulum indicated by its x and y coordinates. One knows that x and y are not arbitrary, they are constrained by the length of the pendulum and the position it is hanged from. More complicated field theories, like electromagnetism or Yang-Mills theories are also formulated in terms of redundant gauge variables and there are constraints between them. When one quantizes theories, the constraints have to be promoted to quantum relations between operators, and this is typically problematic.

This talk advocates for an approach to quantum gravity in which one increases the level of redundancy by introducing extra variables with extra constraints. The resulting theories are equivalent to the original ones as classical theories, but their quantization can be more favorable. The idea is not entirely new, it has been carried out more or less implicitly in quantizations of gravity in three dimensions (or two spatial and one time dimension). In three dimensions the Einstein equations imply all space-times are flat, so the resulting theories are relatively simple to handle. The talk proposes following a similar route for gravity in three spatial and one time dimensions, as we think the real universe has. There are numerous technical issues that need to be overcome to complete this approach and this talk addresses some of them. Among them, implementing the new constraints implied by the new formulation. However, the constraints of the traditional formulation of gravity, that have proven to be very problematic, appear geometrically very transparent in the current approach.