  A finite Hilbert space can be associated to a periodic phase space, that is,
a torus. A finite subgroup of operators corresponding to reflections and
translations on the torus form respectively the basis for the discrete Weyl
representation, including the Wigner function, and for its Fourier conjugate,
the chord representation. They are invariant under Clifford transformations and
obey analogous product rules to the continuous representations, so allowing for
the calculation of expectations and correlations for observables. We here
import new identities from the continuum for products of pure state Wigner and
chord functions, involving, for instance the inverse phase space participation
ratio and correlations of a state with its translate. New identities are
derived involving {\it transition} Wigner or chord functions of transition
operators $\ket{\psi_1}\bra{\psi_2}$. Extension of the reflection and
translation operators to a doubled torus phase space leads to the
representation of superoperators and so to the construction of the propagator
of Wigner functions from the Weyl representation of the evolution operator.
