The master constraint (see below) does not suffer from these problems and as such offers a way of connecting the canonical theory to the path integral formulation. It turns out there are alternative routes to formulating the path integral, however their connection to the Hamiltonian formalism is less clear. One way is to start with the BF theory. This is a simpler theory than general relativity, it has no local degrees of freedom and as such depends only on topological aspects of the fields. BF theory is what is known as a topological field theory. Surprisingly, it turns out that general relativity can be obtained from BF theory by imposing a constraint, BF theory involves a field formula_333 and if one chooses the field formula_177 to be the (anti-symmetric) product of two tetrads  (tetrads are like triads but in four spacetime dimensions), one recovers general relativity. The condition that the formula_177 field be given by the product of two tetrads is called the simplicity constraint. The spin foam dynamics of the topological field theory is well understood. Given the spin foam 'interaction' amplitudes for this simple theory, one then tries to implement the simplicity conditions to obtain a path integral for general relativity. The non-trivial task of constructing a spin foam model is then reduced to the question of how this simplicity constraint should be imposed in the quantum theory. The first attempt at this was the famous Barrett–Crane model. However this model was shown to be problematic, for example there did not seem to be enough degrees of freedom to ensure the correct classical limit. It has been argued that the simplicity constraint was imposed too strongly at the quantum level and should only be imposed in the sense of expectation values just as with the Lorenz gauge condition formula_337 in the Gupta–Bleuler formalism of quantum electrodynamics. New models have now been put forward, sometimes motivated by imposing the simplicity conditions in a weaker sense. Another difficulty here is that spin foams are defined on a discretization of spacetime. While this presents no problems for a topological field theory as it has no local degrees of freedom, it presents problems for GR. This is known as the problem triangularization dependence. Just as imposing the classical simplicity constraint recovers general relativity from BF theory, one expects an appropriate quantum simplicity constraint will recover quantum gravity from quantum BF theory. Much progress has been made with regard to this issue by Engle, Pereira, and Rovelli, Freidel and Krasnov and Livine and Speziale in defining spin foam interaction amplitudes with much better behaviour.