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.
Spera, M., On Some Geometric Aspects of Coherent States, in Antoine, J., Bagarello, F., Gazeau, J. (ed.), Coherent States and Their Applications, Springer, Cham, Cham 2018: <<SPRINGER PROCEEDINGS IN PHYSICS>>, 205 157- 172. 10.1007/978-3-319-76732-1_8 [http://hdl.handle.net/10807/123272]
On Some Geometric Aspects of Coherent States
Spera, MauroPrimo
2018
Abstract
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.
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