cianfa72's latest activity
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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... -
cianfa72 reacted to PeterDonis's post in the thread A A global energy conservation law in general relativity with
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The fact that there is a global conserved energy in a stationary spacetime is a consequence of Noether's theorem, yes. The Komar energy... -
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...
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cianfa72 replied to the thread I Action of an Hermitian unitary operator member of SU(2).No, I haven't. Maybe the fact that in any orthonormal basis the representative of the operator ##S \in SU(2)## , say ##\hat {S}##, has...
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cianfa72 posted the thread I Action of an Hermitian unitary operator member of SU(2) in Quantum Physics.QM uses separable Hilbert spaces as model to represent quantum system's states. Take for instance a 1/2-spin particle: its quantum pure...
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cianfa72 reacted to martinbn's post in the thread I Lie Derivatives vs Parallel Transport with Like.
One reason is that the Lie derivative is not a good directional derivative. Reason being that at a point it doesn't depend only on the...
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cianfa72 reacted to PeroK's post in the thread I Entanglement: is there 'action at a distance' due to measurement? with Like.
It's conceptually clearer to describe this as a system of two particles in an entangled state. See below. Again, it's conceptually...
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cianfa72 replied to the thread I QM Qubit state space representation by Projective Hilbert space.Suppose to perform a Stern-Gerlach experiment to measure the spin of a spin-1/2 particle by orienting the equipment along the z-axis. In...
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The equivalence principle just says that you can't tell the difference between accelerating in deep space and standing on a planet, at...