• DOI:10.1142/S0129055X16500124
• Corpus ID: 119304563

Higher U(1)-gerbe connections in geometric prequantization

@article{Fiorenza2013HigherUC,
  title={Higher U(1)-gerbe connections in geometric prequantization},
  author={Domenico Fiorenza and Christopher L. Rogers and Urs Schreiber},
  journal={Reviews in Mathematical Physics},
  year={2013},
  volume={28},
  pages={1650012}
}

• D. Fiorenza, Christopher L. Rogers, U. Schreiber
• Published 31 March 2013
• Mathematics
• Reviews in Mathematical Physics

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 ∞-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the ∞-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian ∞-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the L∞-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. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.