Quantum Structure of Geometry: Loopy and fuzzy - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: In any attempt to build a quantum theory of gravity, a central issue is tounravel the structure of space-time at the smallest scale. Of particularrelevance is the possible definition of coordinate functions within the theoryand the study of their algebraic properties, such as non-commutativity. Here weapproach this issue from the perspective of loop quantum gravity and thepicture of quantum geometry that the formalism offers. In particular, as weargue here, this emerging picture has two main elements: i) The nature of thequantum geometry at Planck scale is one-dimensional, polymeric with quantizedgeometrical quantities and; ii) Appropriately defined operators correspondingto coordinates by means of intrinsic, relational, constructions becomenon-commuting. This particular feature of the operators, that operationallylocalize points on space, gives rise to an emerging geometry that is also, in aprecise sense, fuzzy.



Author: Alejandro Corichi, Jose A. Zapata

Source: https://arxiv.org/



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