Shape in an Atom of Space: Exploring quantum geometry phenomenology

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde

Strings from Logic

What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom. Strings arise, because these large-N theories are dual to string theories. These ``logical quantum field theories'' map theorems into the space of functions of two parameters: N and the coupling constant. Undecidable theorems might be related to nonperturbative field theory effects.Comment: Talk, 19 pp, 7 figure

Dirac lattice

We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations above point-like Fermi surface. Together with the Dirac fermionic field an effective space-time metric is also emerging. We analyze the conditions for such Fermi points to appear in general, paying special attention to the cases of two and three spacial dimensions.Comment: 26 pages, 4 figures; typo and grammatical corrections, new reference(s) added, version accepted for publicatio