Gerbes in Geometry, Field Theory, and Quantisation

This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms...

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Autor principal:	Bunk Severin
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	bundle gerbes higher geometry functorial field theory wzw model 2-plectic geometry derived geometric quantisation 53c08 53d50 57r56 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/fe53a03b347e44f198f1844fac466d19
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id	oai:doaj.org-article:fe53a03b347e44f198f1844fac466d19
record_format	dspace
spelling	oai:doaj.org-article:fe53a03b347e44f198f1844fac466d192021-12-05T14:10:45ZGerbes in Geometry, Field Theory, and Quantisation2300-744310.1515/coma-2020-0112https://doaj.org/article/fe53a03b347e44f198f1844fac466d192021-06-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0112https://doaj.org/toc/2300-7443This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted symplectic forms. This generalises earlier applications of gerbes to the prequantisation of quasi-symplectic groupoids.Bunk SeverinDe Gruyterarticlebundle gerbeshigher geometryfunctorial field theorywzw model2-plectic geometryderived geometric quantisation53c0853d5057r56MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 150-182 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bundle gerbes higher geometry functorial field theory wzw model 2-plectic geometry derived geometric quantisation 53c08 53d50 57r56 Mathematics QA1-939
spellingShingle	bundle gerbes higher geometry functorial field theory wzw model 2-plectic geometry derived geometric quantisation 53c08 53d50 57r56 Mathematics QA1-939 Bunk Severin Gerbes in Geometry, Field Theory, and Quantisation
description	This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted symplectic forms. This generalises earlier applications of gerbes to the prequantisation of quasi-symplectic groupoids.
format	article
author	Bunk Severin
author_facet	Bunk Severin
author_sort	Bunk Severin
title	Gerbes in Geometry, Field Theory, and Quantisation
title_short	Gerbes in Geometry, Field Theory, and Quantisation
title_full	Gerbes in Geometry, Field Theory, and Quantisation
title_fullStr	Gerbes in Geometry, Field Theory, and Quantisation
title_full_unstemmed	Gerbes in Geometry, Field Theory, and Quantisation
title_sort	gerbes in geometry, field theory, and quantisation
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/fe53a03b347e44f198f1844fac466d19
work_keys_str_mv	AT bunkseverin gerbesingeometryfieldtheoryandquantisation
_version_	1718371757954433024

Gerbes in Geometry, Field Theory, and Quantisation

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