Classical and quantum mechanics on the unit ball in \({\mathbb{C}}^ n\) (Q1100324)

By the third author [Commun. Math. Phys. 114, 557-597 (1988)] it was shown that when the phase space of a classical physical system admits a Kähler structure it can often be embedded into the projective Hilbert space of quantum states. This paper applies these ideas to the unit ball in \({\mathbb{C}}^ n\) which is treated as a SU(1,n) equivariant, strictly Hamiltonian phase space. The coherent states are explicitly calculated and their connection with path integrals explained.