Yakov Neiman 2009 Class. Quantum Grav. 26 245001 doi:10.1088/0264-9381/26/24/245001
Yakov Neiman
Show affiliationsWe argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy regularization is assumed. We note a natural dependence of the Hilbert space on a codimension-2 boundary surface. The Hilbert product is defined dynamically, in terms of transition amplitudes which are described by a path integral. We show that a canonical basis is incompatible with these assumptions, which opens the possibility for a smaller Hilbert-space dimension than canonically expected. We argue further that this dimension may decrease with surface area at constant volume, hinting at holographic area proportionality. We draw comparisons with other approaches and setups, and propose an interpretation for the non-holographic space of graviton states at asymptotically Minkowski null infinity.
Issue 24 (21 December 2009)
Received 8 May 2009, in final form 18 October 2009
Published 16 November 2009
Yakov Neiman 2009 Class. Quantum Grav. 26 245001
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