Recent content by Chain

Continuous maps always map convergent sequences to convergent sequences. So if the map T \mapsto T^* is strongly continuous then it should map any strongly convergent sequence to another strongly convergent sequence. Now I see the issue, we know the map will take a norm convergent sequence...

But then if what you say is true then surely the map T \mapsto T^* is also continuous in the strong operator topology which contradicts what is says in Simon and Reed. Thank you for the quick response! EDIT: In Simon and Reed it says the map T \mapsto T^* is continuous in the weak and norm...

If a sequence of operators \{T_n\} converges in the norm operator topology then: $$\forall \epsilon>0$$ $$\exists N_1 : \forall n>N_1$$ $$\implies \parallel T - T_n \parallel \le \epsilon$$ If the sequence converges in the strong operator topology then: $$\forall \psi \in H$$...

Thank you for all the responses! My problem was that {S, empty set} is a finite cover of S since the union of S and the empty set is just S. Then surely {S} is a subset of {S, empty set} in which case is this not a finite subcover? I think the answer to this problem lies with remark...

So the definition I have seen is: Given a topological space <S,F> it is compact if for any cover (union of open sets which is equal to S) there exists a finite subcover. By the definition of a topological space both S and the empty set must belong to the family of subsets F. Wouldn't <S, empty...

So the problem is in the last step where I swap the order of differentiation because it is not possible to find time as a function of position? I guess the proper expression for the differential of acceleration with respect to a spatial coordinate is: \partial a(t(x)) / \partial x =...

So I'm looking at the hessian of the Newtonian potential: \partial^2\phi / \partial x_i \partial x_j Using the fact that (assuming the mass is constant): F = m \cdot d^2 x / d t^2 = - \nabla \phi This implies: \partial^2\phi / \partial x_i \partial x_j = -m \cdot...

Thanks for the reply abitslow. Yeah I didn't think about that, I guess spin up can be written as a superposition of different states in a different basis so my definition of full polarisation is wrong. When you say using terms like full or weak to describe the situation are not useful...

Ah thank you DrChinese that clarifies some things. Doesn't this still mean that a particle that isn't observed at all still has no polarisation though? My problem is that in collider experiments they talk about the production polarisation of certain particles and I was wondering where these...

Hi, I'm trying to understand particle polarization. To my understanding if a particle is in a pure quantum state with non-zero spin (i.e. spin up) then it is fully polarized. If it is in a superposition of different spin states then it is weakly polarized and if its properties are uniform...

That's interesting, according to the pdg its branching fraction is still of the same order as the FCNC decay modes which occur at the one-loop level. Surely if it occurs at the tree level it should have a higher branching fraction?

Ah >__< okay thank you for the help :)

Ah okay I'll look into that. When you say "what else would it emit to get the in state to the out state?" do you mean what else would it emit to have a di-lepton pair in the final state? Because what I'm asking is does there have have to be a photon or di-lepton pair in the final state or is a...

Hi, I'm trying to understand the process in the Feynman diagram below: [/PLAIN] Specifically I'm wondering if the virtual quark has to emit a photon / Z boson and if so why? Also I don't understand how the photon / Z boson decays to a di-lepton pair since surely this violates spin...

Ah okay thank you that clears things up.