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On Some Geometric Aspects of Coherent States

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Coherent States and Their Applications

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 205))

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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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Acknowledgements

The author is grateful to J.-P. Antoine, F. Bagarello and J.-P. Gazeau, Organizers of the Workshop “Coherent States and their Applications: A Contemporary Panorama”, held at CIRM, Marseille (Luminy), 14th–18th November 2016, and dedicated to the memory of our most dear common friend and colleague S. Twareque Ali, for the opportunity given to him to present a talk therein, for the excellent scientific level and atmosphere, and for partial financial support. He also acknowledges partial support from D1-funds (Catholic University) (ex 60% Italian MIUR funds). This work has been carried out within the activities of INDAM (GNSAGA). The author is also grateful to the Referees for careful and critical reading. Finally, he also wishes to thank the staff of CIRM for providing, as usual, optimal working conditions in a fantastic natural landscape.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica Niccolò Tartaglia, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121, Brescia, Italy

    Mauro Spera

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  1. Mauro Spera
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Correspondence to Mauro Spera .

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Editors and Affiliations

  1. Institut de recherche en mathématique et physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine

  2. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Palermo, Italy

    Fabio Bagarello

  3. Laboratoire APC, Paris Diderot University, Paris, France

    Jean-Pierre Gazeau

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Spera, M. (2018). On Some Geometric Aspects of Coherent States. In: Antoine, JP., Bagarello, F., Gazeau, JP. (eds) Coherent States and Their Applications. Springer Proceedings in Physics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-76732-1_8

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