On Some Geometric Aspects of Coherent States

In this note we review some issues in the geometrical approach to coherent states (CS). Specifically, we reformulate the standard (compact, simple) Lie group CS by placing them within the frameworks of geometric quantum mechanics and holomorphic geometric quantization and establishing a connection with Fisher information theory. Secondly, we briefly revisit the CS-approach to the Hilbert space Grassmannian and the KP-hierarchy and finally we discuss the CS aspects emerging in the geometric approach to Landau levels via the Fourier-Mukai-Nahm transform.