Has Hilbert transform ever been used in Quantum Theory?

[mad mathematician]

Anyone knows if this transform ever been used in QT directly?

I just had seen it in one advanced course in complex analysis which I failed and in singals analysis courses in EE.
But in all the books and courses in QT never I had seen this transform being used.

Perhaps in Quantum Control theory...
https://en.wikipedia.org/wiki/Hilbert_transform

 

[otennert]

In scattering theory, when you consider the so-called (complex-valued) Jost functions $F_l(k)$, the dispersion relations relate the real and the imaginary parts of $F_l(k) -1$. And the specific form of these relations make each the Hilbert transforms of the other. Just google for Jost functions and dispersion relations.

 

[DrDu]

I used it once in a perturbation expansion of a unitary operator. It was somewhat simpler than the usual expansion of the complex exponential. But I forgot the details.

 

[Philip Koeck]

Anyone knows if this transform ever been used in QT directly?

I just had seen it in one advanced course in complex analysis which I failed and in singals analysis courses in EE.
But in all the books and courses in QT never I had seen this transform being used.

Perhaps in Quantum Control theory...
https://en.wikipedia.org/wiki/Hilbert_transform

The Kramers Kronig relations in (quantum) optics.

Edit: Looks like the KK relations are used for almost everything:
https://en.wikipedia.org/wiki/Kramers–Kronig_relations