Re: 10 questions on QM postulates

Arnold Neumaier wrote:

> Almost everything they do in the nonrelativistic regime
> can be made rigorous in the rigged Hilbert space, so they fare right
> even when they imagine wrongly that they work in a Hilbert
> space. Thus they get away with their bad practices.
> What they call 'Hilbert space' _is_ in fact always a
> rigged Hilbert space; they just don't know and don't care.

Yeah, that's right. So in other words, I have to "smear" the usual Fock
states with wavepackets to get vectors in the Hilbert space. If one is
honest, one must do this all the time, I agree with you, especially
when deriving the LSZ-reduction formula and the like.

On the other hand, isn't this what the axiomatic quantum-field theorists
try to do, and they never could get a definite answer to the question
of a rigorous treatment of interacting relativististic QFTs? I don't
know much about the current status of this endeaver, but most
physicists, I know and work with, do not think very high of this quite
mathematical branch of QFT. One once said about it: "Ah, that's very
deep stuff, but they cannot explain more than the free particle. They
can not even prove QED to exist." Is this still true?

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@xxxxxxxxxxxxx

.

Relevant Pages

  • Re: Dynamical Systems and Expansion-Contraction
    ... Irreversibility and Causality, Springer: ... which Antoine defines as in my notation: ... RHS = A triplet where H is a Hilbert space, A is dense ... The Rigged Hilbert Space formalism is able to deal with continuous ...
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  • Re: 10 questions on QM postulates
    ... >>rigged Hilbert space; they just don't know and don't care. ... A working physicists can therefore ignore that part of QFT. ... Arnold Neumaier ...
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  • Re: 10 questions on QM postulates
    ... part of the right Gelfand triple = rigged Hilbert space. ... This is the name for a triple H in Hbar in H^* of vector spaces, where Hbar is a Hilbert space, H a dense 'nuclear' subspace and H^* its dual space. ... can be made rigorous in the rigged Hilbert space, ...
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