Introduction to Coherent States

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Didier Robert, Monique Combescure

In previous Chapters we have considered coherent states systems for bosons and for fermions separately. Here we introduce super-spaces where it is possible to consider simultaneously bosons and fermions. Our aim is to give a short introduction to this deep and difficult subject by considering some elementary examples where coherent states and quantization are involved.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Angel Ricardo Plastino, And M.C. Rocca

Handling coherent states by undergraduates students may be a hard task, as they have to deal with Glauber's series $e^{-\frac {|\alpha|^2} {2}}\sum\limits_{n=0}^\infty\frac {\alpha^n} {\sqrt{n!}}\phi_n(x)$. We show here that the task can be greatly simplified by introduction of a novel compact formula for Glauber coherent states employed in [ Int. J. Mod. Phys. B {\bf 31} (2017) 175051]. This expression is obtained by solving the basic differential equation associated to coherent states $a|\alpha>=\alpha|\alpha>$.

Dorje C. Brody, Eva-Maria Graefe

The state spaces of generalized coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of the underlying state space into higher dimensional state spaces. This construction is applied to the parameterization of generalized coherent states, which is useful for practical calculations, and provides an elementary combinatorial approach to the geometry of the coherent state space. The results are extended to Hilbert spaces with indefinite inner products, leading to the introduction of a new kind of generalized coherent states.

Peter W. Milonni, Michael Martin Nieto