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In this screenshot of a paper I am reading, I have the following question:

1.What is a $SU(1,1)$ group and how do we find its generators?

2.From the expression for the Hamiltonian $\hat{H}$, how do we infer the form of the operator $\hat{U}(t,0)$ as in the equation $6$?

3.How can I write a similar definition of $\hat{U}$ for time $t_0$ to $t$ rather than $0$ to $t$?

P.S. Any resource recommendation would be appreciated. .

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