# nLab prequantum 0-bundle

Contents

## Applications

#### Bundles

bundles

fiber bundles in physics

## Constructions

#### Quantum field theory

functorial quantum field theory

# Contents

## Idea

In higher differential geometry the notion of connection on a bundle and in particular that of circle bundle with connection is refined to a tower of notions of circle n-bundles with connection for all $n \in \mathbb{N}$. In particular also the degenerate case of $n = 0$ is defined and fits into this tower: a 0-bundle is simply a function with values in the given structure group (e.g. the circle group $U(1)$).

Moreover, for a prequantum field theory defined by an extended Lagrangian there is such a circle (n-k)-bundle with connection for each closed manifold of dimension $k$, called the prequantum (n-k)-bundle. For $n = k$ this is the action functional of the theory. Hence the action functional may be thought of as the prequantum 0-bundle of an extended prequantum field theory.

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

## References

Lecture notes with more details are in the section Lagrangians and Action functionals of

Created on January 5, 2013 at 19:56:26. See the history of this page for a list of all contributions to it.