  Topological materials are characterized by an electronic band structure with
nontrivial topological properties. In this paper, we introduce a basis of
operators for the linear space of operators spanned by charge-neutral fermion
bilinears. These band projected density operators are constructed using
directly the eigenfunctions of the electronic energy band structure and there
is no need to assume a flat Berry curvature. As a result, our set of operators
has a wider range of validity and is sensitive to physical phenomena which are
not detectable in the flat curvature limit. In particular, we show that the
Berry monopole configuration of Weyl semimetal give rises to a nonvanishing
Jacobiator for these band projected density operators, implying the emergence
of nonassociativity at the location of the Weyl nodes. The resulting
nonassociativity observes the fundamental identity, the defining property of
the Nambu bracket and so one may call this a nonassociative Nambu geometry. We
also derive the corresponding uncertainty principle.
