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arXiv · hep-th/0209044

Quantum Cosmology and Conformal Invariance

B. Pioline·A. Waldron
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Abstract

According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the universe is the zero-energy eigenmode of the Hamiltonian, also known as the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models is constructed, based on the quantization of nilpotent coadjoint orbits, where the conformal group is enhanced to an ADE non-compact group for which the spherical vector is known.

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B. Pioline, A. Waldron. 2003-01-20. Quantum Cosmology and Conformal Invariance. https://doi.org/10.1103/physrevlett.90.031302

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