In the previous post, I mentioned the intuition of Fredholm determinant for trace class operator, which is . When it comes to Hilbert-Schmidt determinant, which is , that definition(let’s call it ) may fail since trace of H-S operator my be infinity. So we need to come up with another definition(let’s call it ) for H-S operator that makes sense.

The intuition is that consider the eigen values of a H-S matrix , say ,notice that for , so we can define

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