Quantum Mechanics in a Rotating Frame

The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non relativistic limit by a simple treatment. By taking the low energy limit of the Dirac equation with a spin connection, we obtain the Hamiltonian for the rotating frame, which gives rise to all the phase shifts discussed before. Furthermore, we obtain a new phase shift due to the spin-orbit coupling.