cianfa72's latest activity
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cianfa72 reacted to PeroK's post in the thread I Validity of identical eigenfunction of commutating operators with
Like.
All Hermitian operators commute with ##I##. And every vector is an eigenvector of ##I##. This is wrong. There must be a common... -
cianfa72 replied to the thread Announcement Please welcome berkeman as PF Admin.Very good, congratulations !
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cianfa72 reacted to fresh_42's post in the thread I 2-sphere intrinsic definition by gluing disks' boundaries with Like.
The quotient building is the identification of certain points in ##D_+## with certain points in ##D_-.## You have to show that these...
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cianfa72 replied to the thread I 2-sphere intrinsic definition by gluing disks' boundaries.Yes of course. From the definition of ##f## given in #2 it takes the same value (##f=0##) on the pair of points in ##D_+## and ##D_-##...
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cianfa72 replied to the thread I 2-sphere intrinsic definition by gluing disks' boundaries.Ok, coming back to the OP, just to be clear, what is a bijective continuos map is the function ##\tilde f## resulting by passing ##f##...
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cianfa72 replied to the thread I 2-sphere intrinsic definition by gluing disks' boundaries.I was thinking as follows: call ##D_{+}## the disk of radius 1 centered at the origin of ##\mathbb R^2## and ##D_{-}## the disk of...
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cianfa72 posted the thread I 2-sphere intrinsic definition by gluing disks' boundaries in Topology and Analysis.A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk...
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cianfa72 reacted to PeterDonis's post in the thread A A global energy conservation law in general relativity with Like.
The fact that there is a global conserved energy in a stationary spacetime is a consequence of Noether's theorem, yes. The Komar energy...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).Eventually I found a counterexample to my question in the OP. Take the following qubit state given in the abstract ##\mathcal H_2##...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).Here my argument: a point on the Bloch sphere $$\ket{\psi} = \cos {(\theta /2)}\ket{\uparrow} + e^{j\phi}\sin {(\theta /2)}...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).Ah yes, you are right :rolleyes: . So, which is the difference in applying an element of SU(2) vs an element of U(2) to the state...
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cianfa72 reacted to martinbn's post in the thread I Action of an Hermitian unitary operator member of SU(2) with Like.
##S## is an element of ##SU(2)##, hence it is an element of ##U(2)##.
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cianfa72 reacted to PeterDonis's post in the thread I Action of an Hermitian unitary operator member of SU(2) with Like.
Why? All you know at this point is that, for any element ##T## of ##U(2)##, ##T = e^{i \theta} S##, where ##S## is an element of...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).Sorry, I meant a unit vector (norm 1). Suppose there was an "hidden phase" inside ##S \in SU(2)##, then ##S = e^{j\theta} S', S' \in...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).As far as I can tell, any element ##T \in U(2)## is given as ##T = e^{j\phi} S## for some ##\phi## and ##S \in SU(2)##. For any...