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Homotopy Colimits and Global Observables in Abelian Gauge Theory

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Abstract

We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

  2. Maxwell Institute for Mathematical Sciences, Edinburgh, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

  3. The Tait Institute, Edinburgh, UK

    Marco Benini, Alexander Schenkel & Richard J. Szabo

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  1. Marco Benini
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  2. Alexander Schenkel
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  3. Richard J. Szabo
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Correspondence to Alexander Schenkel.

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Report No. EMPG-15-04.

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Benini, M., Schenkel, A. & Szabo, R.J. Homotopy Colimits and Global Observables in Abelian Gauge Theory. Lett Math Phys 105, 1193–1222 (2015). https://doi.org/10.1007/s11005-015-0765-y

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