Abstract :
A conjecture is made as to how to quantize topological image theory. We study a Hamiltonian decomposition of Hitchinʹs 7-dimensional action and propose a formulation for it in terms of 13 first class constraints. The theory has 2 degrees of freedom per point, and hence is diffeomorphism invariant, but not strictly speaking topological. The result is argued to be equivalent to Hitchinʹs formulation. The theory is quantized using loop quantum gravity methods. An orthonormal basis for the diffeomorphism invariant states is given by diffeomorphism classes of networks of two-dimensional surfaces in the six-dimensional manifold. The Hamiltonian constraint is polynomial and can be regulated by methods similar to those used in LQG.
