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Letters in Mathematical Physics

, Volume 105, Issue 9, pp 1193–1222 | Cite as

Homotopy Colimits and Global Observables in Abelian Gauge Theory

  • Marco Benini
  • Alexander Schenkel
  • Richard J. Szabo
Article

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.

Keywords

Abelian gauge theory global configurations and observables chain complexes homotopy limits and colimits 

Mathematics Subject Classification

70S15 81T13 55U15 55N20 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Marco Benini
    • 1
    • 2
    • 3
  • Alexander Schenkel
    • 1
    • 2
    • 3
  • Richard J. Szabo
    • 1
    • 2
    • 3
  1. 1.Department of MathematicsHeriot-Watt UniversityEdinburghUK
  2. 2.Maxwell Institute for Mathematical SciencesEdinburghUK
  3. 3.The Tait InstituteEdinburghUK

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