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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • 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

  • UT code for WoS article

    000383237600001

  • EID of the result in the Scopus database

    2-s2.0-84979261693