There seems to be many books on Relativistic Quantum Mechanics (I’ve never read them), however, I seem to remember from Brian Greene’s “Elegant Universe” that QM and relativity theory were incompatible. How do RQM books solve the locality problem? What am I missing here??
QM and relativity as a whole are incompatible, but QM and special relativity are not. Dirac formulated the Dirac equation in 1928 and it’s essientally a relativistically corrected version of the Schroedinger equation.
Superstring theory and more recently, M-theory go a long way towards uniting QM and General Relativity. Especially under the overarching construct of M-theory, which incorporates string-based 11-dimensional supergravity, this new way of thinking about the universe doesn’t merely explain gravity, but requires it, something no previous theory had done. This is very well explained in the last half of The Elegant Universe. As far as the mathematics behind it, don’t ask me.
What MC said. Plus, the modern view is that space time can be viewed as locally flat–that is, compatible with special relativity. That’s the relativity of “relativistic quantum mechanics.”