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

• URL: http://arxiv.org/abs/2311.16385v3
• Date: Fri, 12 Jan 2024 09:03:46 GMT
• Title: A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra
• Authors: Nicola Pranzini
• Abstract summary: We show the emergence of a semi-classical behaviour from the set of coherent states. We verify that it always happens when some parameter, depending on the algebra and its representation, becomes large.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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