"I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space anymore." - John von Neumann

▲

kdavis 7 hours ago | parent [-]

Surprising that he could have that intuition in 1935, before the Unruh effect was known of, before AQFT was invented, and really before most of QFT was formulated.

But then again, he was John von Neumann.

▲

empiricus 5 hours ago | parent [-]

I thought QFT is using hilbert space still?

▲

kdavis 2 hours ago | parent | next [-]

Hawking radiation and the Unruh effect both rely upon the fact that there is no absolute Hilbert space in which QFT unfolds, the Hilbert space used is observer dependent.

For example, in the Unruh effect an inertial observer sees the vacuum in their Hilbert space as having no particles. However, a uniformly accelerating observer sees that same vacuum as containing particles.

This state of affairs is addressed via algebraic quantum field theory (AQFT), which doesn't take a Hilbert space as the primary thing one starts with, but views Hilbert spaces as derived concepts.

▲

senderista 5 hours ago | parent | prev [-]

google "Fock space"

	▲	freehorse 3 hours ago \| parent [-]
		Aren't Fock spaces still hilbert spaces?