Preconjugate variables $X$ have commutation relations with the energy-momentum $P$ of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes, we present a study of them here. Interesting examples $X$ can be found via geometry—motions on the mass shell for massive and massless systems—and via group theory—invariance under special conformal transformations of the mass shell and light cone, respectively. Both find representations on Fock space. We work mainly in ordinary four-dimensional Minkowski space and spin zero. The limit process from nonzero to vanishing mass turns out to be nontrivial and leads naturally to wedge variables. We point out some applications and extensions to more general spacetimes. In a companion paper, we discuss the transition to conjugate pairs.

• Received 1 June 2016

DOI:https://doi.org/10.1103/PhysRevD.94.065007