Higher U(1)-gerbe connections in geometric prequantization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00461871" target="_blank" >RIV/67985840:_____/16:00461871 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/S0129055X16500124" target="_blank" >http://dx.doi.org/10.1142/S0129055X16500124</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0129055X16500124" target="_blank" >10.1142/S0129055X16500124</a>
Alternative languages
Result language
angličtina
Original language name
Higher U(1)-gerbe connections in geometric prequantization
Original language description
We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant–Souriau $infty$-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the $infty$-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian $infty$-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the $L_infty$-algebra extension of Hamiltonian vector fields - which is the higher Poisson bracket of local observables - and show that it is equivalent to the construction proposed by the second author in n-plectic geometry.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reviews in Mathematical Physics
ISSN
0129-055X
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
6
Country of publishing house
SG - SINGAPORE
Number of pages
72
Pages from-to
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UT code for WoS article
000383237600001
EID of the result in the Scopus database
2-s2.0-84979261693