Higher geometric prequantum theory

An article that we have written:

on the higher geometric refinement of prequantum field theory and geometric prequantization formulated generally in cohesive higher geometry.

In the companion article L-∞ algebras of local observables from higher prequantum bundles we discuss the L-∞ algebraic aspects in more detail. See also the discussion at higher Atiyah groupoid.

For more background see


Applications include


We develop the refinement of geometric prequantum theory to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show how there is canonically a tower of higher “gauge groupoids” assigned to a higher prequantization and establish the higher and integrated Kostant-Souriau extension of higher Hamiltonian symplectomorphisms fairly generally. 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 in n-plectic geometry proposed by Rogers. Finally we indicate examples of applications of higher prequantum theory in the extended geometric quantization of local quantum field theories and specifically in string geometry.

Revised on November 24, 2015 08:26:58 by Urs Schreiber (