Re: 10 questions on QM postulates

Hendrik van Hees wrote:

> Arnold Neumaier wrote:
>
>>In general, the domain of the adjoint can be larger or smaller.
>>For example, the adjoint of an annihilation operator has only
>>the zero vector in its domain.
>
> Could you explain this a little bit? Is the point that the usual Fock
> states over a one-particle basis are not real Hilbert-space vectors but
> live in the larger space of "generalized" funcions, i.e. the dual of
> the nuclear space of the G'elfand triple?

It depends what one calls 'usual' Fock states. The state
|x_1:N> = |x_1,...,x_N>
is not in the Hilbert Fock space, for the same reason for which
|x> is not in the 1-particle Hilbert space. It is only a
distribution.

The Hilbert Fock space is made of all wave functions
psi = sum_N integral dx_1:n psi_N(x_1:N) |x_1,...,x_N>
with finite
<psi|psi> = sum_N |psi_N|^2/N!


Arnold Neumaier

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