Higher U(1)-gerbe connections in geometric prequantization

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Higher U(1)-gerbe connections in geometric prequantization

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Higher U(1)-gerbe connections in geometric prequantization

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Reviews in Mathematical Physics

ISSN

0129-055X

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

72

Strana od-do

—

Kód UT WoS článku

000383237600001

EID výsledku v databázi Scopus

2-s2.0-84979261693