2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53149We investigate the possibility of defining states on timelike hypersurfaces in quantum field theory. To this end we consider hyperplanes in the real massive Klein-Gordon theory using the Schroedinger representation. We find a well defined vacuum wave functional, existing on any hyperplane, with the remarkable property that it changes smoothly even under Euclidean rotation through the light-cone. Moreover, particles on timelike hyperplanes exist and occur in two variants, incoming and outgoing, distinguished by the sign of the energy. Multi-particle wave functionals take a form similar to those on spacelike hypersurfaces. The role of unitarity and the inner product is discussed.4 pages, 2 figures, LaTeX + revtex4 + eepicHigh Energy Physics - TheoryQuantum Physicstext