Neil Turok
speaker
2,693 appearances
2 recordings
1 series
first heard Apr 2025
last heard 22 Jun
Neil Turok’s voice in public audio — every appearance, attributed to the second.
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Appearances
Krine was interested in it because he was studying differential operators.
He's a functional analyst.
And so normally when you consider eigenvalues in the Schrodinger equation or whatever, you know, you very often make the assumption that the space of functions is a Hilbert space.
But Krein said, you know, let's drop that assumption.
Let's allow these negative norms in our functional analysis.
And what he discovered is you can prove all kinds of additional things.
So this mathematical concept was sort of lying around in the literature, just waiting to be used.
And as far as I know, nobody else ever used it.
So indeed, it is a pseudo-Hilbert space.
It's nothing but that.
Yes.
So you mentioned BRST and Fadi Popov.
So that's very good because physicists are actually very used to working in pseudo-Hilbert spaces.
That's what these mathematical ghosts live in.
But the usual prescription is you think you're in this big space, which has both positive and negative and null states.
Then you perform a projection and you say there's a physical subspace where everything is positive.
You use this bigger space to prove certain things.
You basically respect more symmetry by working in this big space, but ultimately you project onto a physical subspace and that's a Hilbert space.
People construct transition amplitudes, they actually sum over all these unphysical directions, but at the end of the day, they do a projection onto the physical sub-suite.
What our construction does is a generalization of that, which is actually more economical.
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