DarMM
Science Advisor
Gold Member
- 2,369
- 1,408
First of all you said this:A. Neumaier said:I know all this. But you were referring to the addition of kets, not of states (linear functionals). A sum of kets is always a pure state (in the Hilbert space of the ket). My question was how it is possible that you refer to it as a mixed state. Or was this only a slip of the pen?
That's not true right? A mixed state may be a vector state in the GNS Hilbert space, but not a pure state.I understand how a mixed state can be pure in a bigger Hilbert space constructed by the GNS construction
Secondly a sum of kets is not a pure state precisely in the case where both belong to different superselection sectors. Unless you are have a certain precise definition of Hilbert space in mind.