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Calculus structure on the Lie conformal algebra complex and the variational complex
School of Mathematical Sciences, University of Adelaide.
2011 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 5Article in journal (Refereed) Published
Abstract [en]

We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [A. De Sole and V. G. Kac, Commun. Math. Phys. 292, 667 (2009)]. A special case of this construction is the variational calculus, for which we provide explicit formulas.

Place, publisher, year, edition, pages
2011. Vol. 52, no 5
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-24542DOI: 10.1063/1.3580676ISI: 000291106000035OAI: oai:DiVA.org:kth-24542DiVA: diva2:351689
Note
QC 20100915. Updated from submitted to published 20120326. Previous title: Calculus structure on the Lie conformal algebra complexAvailable from: 2010-09-15 Created: 2010-09-15 Last updated: 2012-03-26Bibliographically approved
In thesis
1. Abelian Extensions, Fractional Loop Group and Quantum Fields
Open this publication in new window or tab >>Abelian Extensions, Fractional Loop Group and Quantum Fields
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the theory of Lie group extensions, Lie conformal algebras and twisted K-theory, in the context of quantum physics. These structures allow for a mathematically precise description of certain aspects of interacting quantum field theories. We review three concrete examples, namely symmetry breaking (or anomalies) in gauge theory, classification of D-brane charges in string theory and the formulation of integrable hierarchies in the language of Poisson vertex algebras. The main results are presented in three appended scientific papers.

In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension.

In the second paper we introduce the fractional loop group LqG, that is the group of maps from a circle to a compact Lie group G, with only a small degree of differentiability q ε R+ in the Sobolev sense. We construct abelian extensions and highest weight modules for the Lie algebra Lqg, and discuss an application to equivariant twisted K-theory on G.

In the third paper, we construct a structure of calculus algebra on the Lie conformal algebra complex and provide a more detailed description in the special case of the complex of variational calculus.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. x, 95 p.
Series
Trita-FYS, ISSN 0280-316X ; 2010:13
Keyword
Lie group extensions, Lie conformal algebras, gerbes, twisted K-theory, renormalization, anomalies, D-brane charges, variational complex
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-12155 (URN)978-91-7415-592-1 (ISBN)
Public defence
2010-03-26, FA32, Roslagstullsbacken 21, Albanova universitetscentrum, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20100915Available from: 2010-03-16 Created: 2010-03-15 Last updated: 2010-09-15Bibliographically approved

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