nLab prequantum circle n-bundle

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.

Related concepts

• line 2-bundle

• prequantum n-state

• higher prequantum geometry

• basic bundle gerbe

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