  In the consistent histories formalism one specifies a family of histories as
an exhaustive set of pairwise exclusive descriptions of the dynamics of a
quantum system. We define branching families of histories, which strike a
middle ground between the two available mathematically precise definitions of
families of histories, viz., product families and Isham's history projector
operator formalism. The former are too narrow for applications, and the
latter's generality comes at a certain cost, barring an intuitive reading of
the ``histories''. Branching families retain the intuitiveness of product
families, they allow for the interpretation of a history's weight as a
probability, and they allow one to distinguish two kinds of coarse-graining,
leading to reconsidering the motivation for the consistency condition.

Quantum Physics