Separation of longitudinal and transversal space in the description of twin photons

General expressions for the created two-photon state and the coincidence detection amplitude are derived. The description accounts for entanglement in polarization, in time and frequency, and in the transversal momentum or position amplitudes. Characteristic for spontaneous parametric down-conversion (SPDC) is that the two photons are created at the same location in the crystal, at the same instant of time.