More on doubled Hilbert space in double-scaled SYK

Abstract

We continue our study of the doubled Hilbert space formalism of double-scaled SYK model initiated in [arXiv:2401.07403]. We show that the 1-particle Hilbert space introduced by Lin and Stanford in [arXiv:2307.15725] is related to the doubled Hilbert space ${\mathcal{H}}_0\otimes {\mathcal{H}}_0$ of the 0-particle Hilbert space ${\mathcal{H}}_0$ by some linear isomorphism $\mathcal{C}$. It turns out that the entangler and disentangler appeared in our previous study are given by the dual (or adjoint) of ${\mathcal{C}}^{-1}$ and $\mathcal{C}$.

15 pages

Cited by in corpus (1)

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