Theoretical Physics(DTP)
Physique théorique (DPT)

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Achim KEMPF
University of Waterloo

Towards a Notion of Qubit Density for Quantum Fields in Curved Spacetime

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In the literature, there is much discussion as to whether spacetime is discrete or continuous. In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-bounded music signals are reconstructible perfectly from discrete samples. I will present a generalization of sampling theory to pseudo-Riemannian manifolds. The aim is to provide a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be completely equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.