Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-01-26
Class.Quant.Grav.26:245001,2009
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, 9 eps figures. Added Section VI, improved presentation. Expanded and split the Introduction into two sections. Added
Scientific paper
10.1088/0264-9381/26/24/245001
We 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.
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