A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra

Abstract

We provide a formula for computing the overlap between two Generalized Coherent States of any rank one simple Lie algebra. Then, we apply our formula to spin coherent states (i.e. $\mathfrak{su}(2)$ algebra), pseudo-spin coherent states (i.e. $\mathfrak{su}(1,1)$ algebra), and the $\mathfrak{sl}(2,\mathbb{R})$ subalgebras of Virasoro. In all these examples, we show the emergence of a semi-classical behaviour from the set of coherent states and verify that it always happens when some parameter, depending on the algebra and its representation, becomes large.

9 pages; v1 and v2 include new references

References in corpus (11)

• How to Build the Thermofield Double State
• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
• Entanglement over the rainbow
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Probing the entanglement of operator growth
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Coherent States in Gravitational Quantum Mechanics
• Optimal Quench for Distance-Independent Entanglement and Maximal Block Entropy
• The classical-quantum limit
• Threshold size for the emergence of a classical-like behaviour
• Nielsen complexity of coherent spin state operators