Quantum Mechanics with Non-Unitary Symmetries

This book shows how a minimal modification of postulates of non-relativistic quantum mechanics to allow for non-unitary representations of symmetry groups (Lorentz group in particular), leads to a fully relativistic quantum theory without any of the issues (like negative energies, etc.) that led to the second quantization and QFT. Relativistic treatment of bound states in momentum space is developed and used to calculate decay widths of various composite particles like Positronium or mesons, and then those decay widths are used to calculate various properties of quarks (like their masses or charges) that were previously misunderstood. It is shown that quite a few phenomena in elementary particle physics (like for example neutral kaon mixing, CP symmetry and it's supposed breaking) can be explained purely as a consequence of relativistic invariance and relativistic invariance alone.