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The continuum approach to the BF vacuum: the U(1) case

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arxiv 1705.09836 v2 pith:MCVVGQMC submitted 2017-05-27 gr-qc

Patryk Drobiński , Jerzy Lewandowski This is my paper · ORCID
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keywords quantumapproachcasecontinuumtheoryvacuumconsistencycontains
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abstract

A quantum representation of holonomies and exponentiated fluxes of a $U(1)$ gauge theory that contains the Pullin-Dittrich-Geiller (DG) vacuum is presented and discussed. Our quantization is performed manifestly in a continuum theory, without any discretization. The discretness emerges on the quantum level as a property of the spectrum of the quantum holonomy operators. The new type of a cylindrical consistency present in the DG approach, now follows easily and naturally. A generalization to the non--Abelian case seems possible.

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  1. Quantum geometry from higher gauge theory

    gr-qc 2019-08 conditional novelty 7.0 of 10

    The BFCG-Yetter model and the KBF state sum produce the same single-4-simplex amplitude when evaluated on boundary states called G-networks.

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