“…With a new generation of positronium experiments coming on-line [1,2,3] it is valuable to review the present status of theory and constraints from other processes on the key observables. This we present here, with main emphasis on physics experiments [1,4,5] that can be performed using the new J-PET detector, Jagiellonian Positron Emission Tomograph, being built in Cracow [6]. The J-PET is a new PET device based on plastic scintillators designed for total body scanning in medicine as well as biological applications [7] and fundamental physics research [1] with detection of positronium and (from its decay products) Compton rescattered photons in the detector.…”