An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains
arXiv:1209.3623 · doi:10.1007/s10701-012-9692-2
Abstract
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.
6 pages, accepted for publication in Foundations of Physics; minor changes in accordance with referee's suggestion