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. su(2) algebra), pseudo-spin coherent states (i.e. su(1,1) algebra), and the sl(2,R) subalgebras of Virasoro. In all these examples, we show the emergence of a semi-classical behavior 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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