Homotopy colimits and global observables in abelian gauge theory

Marco Benini; Alexander Schenkel; Richard J. Szabo

doi:10.1007/s11005-015-0765-y

Homotopy colimits and global observables in abelian gauge theory

Marco Benini, Alexander Schenkel, Richard J. Szabo

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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.

Original language	English
Pages (from-to)	1193-1222
Journal	Letters in Mathematical Physics
Volume	105
Issue number	9
Early online date	30 May 2015
DOIs	https://doi.org/10.1007/s11005-015-0765-y
Publication status	Published - Sep 2015

Keywords

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

ASJC Scopus subject areas

Mathematical Physics
Statistical and Nonlinear Physics

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10.1007/s11005-015-0765-y

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Richard Joseph Szabo
- R.J.Szabo@hw.ac.uk
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)

Cite this

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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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AU - Benini, Marco

AU - Schenkel, Alexander

AU - Szabo, Richard J.

N1 - The work of R.J.S. is partially supported by the Consolidated Grant ST/L000334/1 from the UK Science and Technology Facilities Council, and by the Advanced Grant LDTBUD from the European Research Council.

PY - 2015/9

Y1 - 2015/9

N2 - 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.

AB - 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.

KW - Abelian gauge theory

KW - chain complexes

KW - global configurations and observables

KW - homotopy limits and colimits

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DO - 10.1007/s11005-015-0765-y

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EP - 1222

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 9

ER -

Homotopy colimits and global observables in abelian gauge theory

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Richard Joseph Szabo

Cite this