  We provide a comprehensive classification of constraints and degrees of
freedom for variational discrete systems governed by quadratic actions. This
classification is based on the different types of null vectors of the
Lagrangian two-form and employs the canonical formalism developed in
arXiv:1303.4294 [math-ph] (J. Math. Phys. 54, 093505 (2013)) and
arXiv:1401.6062 [gr-qc] (J. Math. Phys. 55, 083508 (2014)). The analysis is
carried out in both the classical and quantum theory and applies to systems
with both temporally varying or constant discretization. In particular, it is
shown explicitly how changes in the discretization, e.g. resulting from
canonical coarse graining or refining operations or an evolving background
geometry, change the dynamical content of the system. It is demonstrated how,
on a temporally varying discretization, constraints, Dirac observables,
symmetries, reduced phase spaces and physical Hilbert spaces become spacetime
region dependent. These results are relevant for free field theory on an
evolving lattice and linearized discrete gravity models.
