# nLab prequantum circle n-bundle

Contents

## Applications

#### Bundles

bundles

fiber bundles in physics

# Contents

## Idea

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 $n \in \mathbb{N}$.

## Associated higher prequantum line bundle

Given an E-infinity ring $E$ and an infinity-representation

$\rho \colon \mathbf{B}^{n-1} U(1) \to GL_1(E)$

we have the associated infinity-bundle

$X \to \mathbf{B}^n U(1)_{conn} \to E Mod$

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)-bundletraditional terminology
$0$differential universal characteristic maplevel
$1$prequantum (n-1)-bundleWZW bundle (n-2)-gerbe
$k$prequantum (n-k)-bundle
$n-1$prequantum 1-bundle(off-shell) prequantum bundle
$n$prequantum 0-bundleaction 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.