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We describe fundamental equations which define the topological ground statesin the lattice realization of the SU(2) BF phase. We introduce a new scalarHamiltonian, based on recent works in quantum gravity and topological models,which is different from the plaquette operator. Its gauge-theoretical contentat the classical level is formulated in terms of spinors. The quantization isperformed with Schwinger's bosonic operators on the links of the lattice. Inthe spin network basis, the quantum Hamiltonian yields a difference equationbased on the spin 1/2. In the simplest case, it is identified as a recursion onWigner 6j-symbols. We also study it in different coherent statesrepresentations, and compare with other equations which capture some aspects ofthis topological phase.

A new Hamiltonian for the Topological BF phase with spinor networks