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An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains

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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.

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Notes

  1. In 1+1 dimensions, this equation reduces to a simple nonlinear Schrödinger equation, Eq. (3) of the present paper.

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Acknowledgements

The author acknowledges M.Bojowald for useful discussions, and the referees for recommending some improvements in the exposition.

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  1. Departamento de Ciência e Tecnologia Aeroespacial (CTA), Divisão de Materiais (AMR), Instituto de Aeronáutica e Espaço (IAE), São Jose dos Campos, Brazil

    Christine C. Dantas

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  1. Christine C. Dantas
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Correspondence to Christine C. Dantas.

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Dantas, C.C. An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains. Found Phys 43, 236–242 (2013). https://doi.org/10.1007/s10701-012-9692-2

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