A new Hamiltonian for the Topological BF phase with spinor networks

Details A new Hamiltonian for the Topological BF phase with spinor networks A new Hamiltonian for the Topological BF phase with spinor networks

2011-10-14

arxiv.org/abs/1110.3272v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

40 pages

Scientific paper

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

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