I'm studying the Chern-Weil Theory in a book that makes a construction to prove that the cohomology class of c(A) is independent of the connection (and yes, I know that there is an alternate proof for that). The author defines the map $\mathcal{P}(\nabla^0,\nabla^1,\ldots,\nabla^q): I(n,\mathbb{C}) \rightarrow \mathcal{A}^*(X)$ as:
\begin{eqnarray} \left\{ \begin{array}{cc} \mathcal{P}(\nabla^0)(P)=\biggl( \displaystyle\frac{i}{2 \pi} \biggr)^{\text{gr} P} \cdot P(K_{\nabla^0}) \ \ \ \ & \ \ \ \text{if} \ q=0 \\ \mathcal{P}(\nabla^0,\nabla^1,\ldots,\nabla^q)(P)=(-1)^{[q/2]} \wp_*^{\Delta^q}(\mathcal{P}(\nabla^{0,1,\ldots,q})) & \ \ \ \text{if} \ q>0 \end{array} \right. \end{eqnarray}
where gr $P$ is the rank of $P$ (if $q=0$) and $\wp_*^{\Delta^q}:\mathcal{A}^*(X \times \mathbb{R}^q) \rightarrow \mathcal{A}^{*-q}(X)$ is the integration along fibers.
Then, he shows that $d(\mathcal{P}(\nabla^0,\nabla^1)(P))=\mathcal{P}(\nabla^0)(P)-\mathcal{P}(\nabla^1)(P)$. When I tried to repeat the proof, I'm having trouble on the term $(-1)^{[q/2]}$ of the definition, because I'm not sure if $[q/2]$ denotes the integer part of $q/2$ or this is just the notation for $(-1)$^$q/2$. I think is the first one, but every reference I search and have for this result uses another proof, and I'm not finding any other material that works with that construction.
My question is: anyone here has seen this definition? If possible, can send me the name of an book/article that can help me understand that?