  Three-body semileptonic $\tau$-decays offer a path to understand the
properties of light hadronic systems and CP symmetry violations through
searches for electric dipole moments. In studies of electro-weak physics, the
hadronic part of the final states has traditionally been described using the
language of form factors. Spectroscopic information, resolved in terms of
orbital angular momentum quantum-numbers, is best being derived from an
explicit decomposition of the hadronic current in the orbital angular momentum
basis. Motivated by the upcoming large data samples from B factories, we
present the full description of the hadronic currents decomposed into quantum
numbers of the hadronic final state using the isobar picture. We present
formulas for orbital angular momenta up to three and apply the rules derived
from hadron spectroscopy to formulate the decay chain of hadronic three-body
systems of arbitrary mass. We also translate this formalism to the language of
form factors and thereby correct insufficiencies found in previous analyses of
three-body hadronic final states.
