The Positronium (Ps) system, a bound state of an electron and a positron, is suitable for testing the predictions of quantum electrodynamics (QED), since its properties can be perturbatively calculated to high accuracy and, unlike the hydrogen system, is not affected by finite size or QCD effects at the current experimental precision level. This makes the Ps atom a good laboratory to test the Fundamental Symmetries of Physics and also search for new particles not included in the Standard Model (SM) of physics.

On one hand, time reversal (T) and CP symmetry violation have never been observed in pure leptonic systems like the Ps atom, and the current experimental limits for CP and CPT violation in the decays of Ps is currently set at the level of 10$^{-3}$, while for C violation are at the level of 10$^{-7}$. These limits are still six and two orders of magnitude lower than the expected precision of 10$^{-9}$ set by photon-photon interactions. Secondly, experiments searching for invisible decays of the Ps triplet state, the ortho-Positronium (o-Ps), which mainly decays to three photons, are being conducted, since they are sensitive to new physics scenarios, e.g. Mirror Matter (MM), a suitable Dark Matter candidate, proposed to restore parity (P) violation. By performing a high precision measurement of the o-Ps lifetime, the accuracy of the present QED calculations can be tested and a search for the invisible decays of the o-Ps can be performed.

These studies are conducted with the novel total-body Positron-Electron Tomograph (PET) scanner at the Jagiellonian University. The J-PET is a large and high precise medical imaging tool, based on the plastic scintillators. It is a high acceptance multi-purpose detector optimized for the detection of photons from positron-electron annihilation and can be used in a broad scope of interdisciplinary investigation, e.g. medical imaging, life-time measurements, quantum entanglement studies with o-Ps, and tests of discrete symmetries.