geometric quantization higher geometric quantization
geometry of physics: Lagrangians and Action functionals + Geometric Quantization
prequantum circle n-bundle = extended Lagrangian
prequantum 1-bundle = prequantum circle bundle, regularcontact manifold,prequantum line bundle = lift of symplectic form to differential cohomology
(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
In higher geometric prequantization (see there for more details for the moment) the notion of prequantum circle bundle is refined to that of a prequantum circle n-bundle with connection for all $n \in \mathbb{N}$.
Given an E-infinity ring $E$ and an infinity-representation
we have the associated infinity-bundle
This is the higher analog of the prequantum line bundle, the higher prequantum line bundle.
See at motivic quantization for more on this.
extended prequantum field theory
$0 \leq k \leq n$ | (off-shell) prequantum (n-k)-bundle | traditional terminology |
---|---|---|
$0$ | differential universal characteristic map | level |
$1$ | prequantum (n-1)-bundle | WZW bundle (n-2)-gerbe |
$k$ | prequantum (n-k)-bundle | |
$n-1$ | prequantum 1-bundle | (off-shell) prequantum bundle |
$n$ | prequantum 0-bundle | action functional |
Last revised on August 21, 2013 at 19:57:22. See the history of this page for a list of all contributions to it.