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Boundedness of quantum observables? 
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#37
Feb311, 04:31 PM

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#38
Feb311, 06:48 PM

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PF Gold
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#39
Feb311, 06:51 PM

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#40
Feb311, 07:06 PM

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What would be interesting from the point of view of ''C* algebra's'' is that you try to extend the GNS construction to nonpositive states, so that you will get Nevanlinna space representations. This requires of course a change in the C* norm identities in the first place, but it might be good to define such generalized algebra's. 


#41
Feb311, 07:11 PM

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I do however agree that the fact that the unbounded operators are so prominent suggests that it would be desirable to start with some kind of algebra of unbounded operators instead. Perhaps there is such an approach, that gives us a rigged Hilbert space in a way that's similar to how the C*algebra approach gives us a Hilbert space. 


#42
Feb311, 07:26 PM

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Careful 


#43
Feb311, 07:37 PM

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#44
Feb311, 07:41 PM

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(bolding by me). That's the von Neumann's projection postulate which pertains to the Copenhagian view of things. It's not universally accepted and other interpretations and axiomatizations of QM completely disregard it. As far as I recall (but if I'm wrong, please correct me), putting an RHS into a QM problem with unbounded operators turns these operators into bounded ones, but of course, not in the original topology of the Hspace, but in the topology of the antidual space in which the original operators will find their eigenvectors. 


#45
Feb311, 08:08 PM

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The language of unbounded / distributional operators can be constructed using foundations built from of bounded operators 


#46
Feb411, 02:44 AM

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#47
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#49
Feb411, 02:51 AM

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#50
Feb411, 02:56 AM

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Instead, one starts with a clean slate figuring a configuration space with an action, or a phase space with a Hamiltonian. Nobody cares there about how it relates to reality  the theory stands for itself though it is inspired by reality. And the examples used are heavily idealized compared to the real thing  they illustrate the math and physics but would get really complicated if one would have to discuss them in the context of reality. 


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Feb411, 02:59 AM

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#52
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#53
Feb411, 03:04 AM

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Careful 


#54
Feb411, 03:27 AM

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