nLab
prequantum circle n-bundle

Context

Geometric quantization

Bundles

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 nn \in \mathbb{N}.

Associated higher prequantum line bundle

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

ρ:B n1U(1)GL 1(E) \rho \colon \mathbf{B}^{n-1} U(1) \to GL_1(E)

we have the associated infinity-bundle

XB nU(1) connEMod 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

0kn0 \leq k \leq n(off-shell) prequantum (n-k)-bundletraditional terminology
00differential universal characteristic maplevel
11prequantum (n-1)-bundleWZW bundle (n-2)-gerbe
kkprequantum (n-k)-bundle
n1n-1prequantum 1-bundle(off-shell) prequantum bundle
nnprequantum 0-bundleaction functional

Revised on August 21, 2013 19:57:22 by Urs Schreiber (150.212.94.100)