Gauge invariance on interaction $U(1)$-bundles

Abstract

The structure of the algebra of gauge-invariant differential forms on the bundle $C\times _{M}E$ is determined, where $p\colon C\rightarrow M$ is the bundle of connections of a $U(1)$-principal bundle $\pi \colon P\rightarrow M$, and $E\rightarrow M$ is the associated bundle to $P$ by the representation $\lambda _{r}$, $r\in \mathbb{N}$, of $U(1)$ on $\mathbb{C}$ given by $\lambda _{r}(z)(w)=z^{r}\,w$, $z\in U(1)$, $w\in \mathbb{C}$.