Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-09-05
Phys.Rev.Lett. 90 (2003) 031302
Physics
High Energy Physics
High Energy Physics - Theory
4 pages, latex2e, uses revtex4
Scientific paper
10.1103/PhysRevLett.90.031302
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.
Pioline Boris
Waldron Andrew
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