A discrete, unitary, causal theory of quantum gravity

Details A discrete, unitary, causal theory of quantum gravity A discrete, unitary, causal theory of quantum gravity

2012-01-12

arxiv.org/abs/1201.2489v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages, 9 figures

Scientific paper

A discrete model of Lorentzian quantum gravity is proposed. The theory is fully background free, containing no reference to absolute space, time, or simultaneity. The states at one slice of time are networks in which each vertex is labelled with two arrows, which point along an adjacent edge, or to the vertex itself. The dynamics is specified by a set of unitary replacement rules, which causally propagate the local degrees of freedom. The inner product between any two states is given by a sum over histories. Assuming it converges, this inner product is proven to be hermitian and fully gauge-degenerate under spacetime diffeomorphisms. At least for states with a finite past, the inner product is also positive. This allows a Hilbert space of physical states to be constructed.

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