nLab
prequantum circle n-bundle

Contents

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

Last revised on August 21, 2013 at 19:57:22. See the history of this page for a list of all contributions to it.