nLab prequantum 0-bundle

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.

Related concepts

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

References

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

• geometry of physics