Coherent States and Duality

Abstract

We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space $\mathcal{C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the points of $\mathcal{C}$ exist when there is an almost complex structure on $\mathcal{C}$. When $\mathcal{C}$ admits a complex structure, such coherent states are globally defined on $\mathcal{C}$. The picture of quantum mechanics that emerges allows to implement duality transformations.

7 pages, LaTeX

References in corpus (2)

• Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics
• Deformation Quantization of Classical Fields

Cited by in corpus (3)

• Semiclassical States for Constrained Systems
• Duality, Quantum Mechanics and (Almost) Complex Manifolds
• Quantum-Mechanical Dualities from Classical Phase Space