  Conservation laws are one of the most generic and useful concepts in physics.
In nonlinear optical parametric processes, conservation of photonic energy,
momenta and parity often lead to selection rules, restricting the allowed
polarization and frequencies of the emitted radiation. Here we present a new
scheme to derive conservation laws in optical parametric processes in which
many photons are annihilated and a single new photon is emitted. We then
utilize it to derive two new such conservation laws. Conservation of
reflection-parity (RP) arises from a generalized reflection symmetry of the
polarization in a superspace, analogous to the superspace employed in the study
of quasicrystals. Conservation of space-time-parity (STP) similarly arises from
space-time reversal symmetry in superspace. We explore these new conservation
laws numerically in the context of high harmonic generation and outline
experimental set-ups where they can be tested.
