What does the real Klein-Gordon Hilbert space look like
You have the big Fock space that is too big, it contains the theories for all kinds of weird vacuum states that can't be reach from the zero one
After applying superselection, what does the Hilbert space look like?
(also I guess the Fock space has all kinds of KG theories for all possible masses or something)
how does one whittle it down and to what
The usual KG Hilbert space can't contain any of those infinite particle states (that can't be reached from the $C^*$ algebra), it can't contain states that aren't on the mass shell or in the wrong time direction
start with the basis for the 1-particle space, which is countable (e.g. use Hermite polynomials in momentum or whatever) and the basis of the full Hilbert space is just that + the basis for the 2-particle space as tensoring the 1-particle space with itself + the basis for the 3-particle space etc.
this is still countable because you've started with a countable basis and the n in n-particle space is also countable - a countable collection of countable things is still countable
the Fock space is built as the direct sum of the n-particle spaces. "direct sum" means any given element only has finitely many non-zero contributions from the individual n-particle spaces
but whether your FBD needs that depends on what you're drawing it for
these diagrams are not ends in themselves, they are a means to solve some specific problem - sometimes you'll be interested in friction forces, sometimes you won't be
Good morning/evening! I am planning to drop a magnet into a copper tube to make luminiscent LEDs as an experiment. I wanted to know would the flux/change in flux depend on the cross-sectional area of the copper tube.
In other words if a magnet is falling into a tube would pipes with bigger area make bigger emf or smaller ones?
I do know that the faradays formula says emf = NASinthetha * dB/dt so can we use that and say theres a direct propotionality?
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@ACuriousMind Wait. I thought you need to include almost all forces involved. Since there is an applied force, I thought you also need to include the frictional force
Real life performance is affected by many things, in general trains tend to go slower and accelerate than the maximum they can do. 0-100 in 410s sounds slow but reasonable
if it's a medium/long distance train with not too many stops, acceleration does not matter too much
09020 - Hw Bandra Spl runs from Haridwar Jn to Ghaziabad, 7 days of the week. The 09020 mail express train departs from Haridwar Jn at 01:30 hrs and arrives at Ghaziabad at 05:59 hrs. The total running duration of 09020 train is 4hr 29min, stopping at 7 stations during the journey.
@Slereah I don't think that's a factor, there's a big gap between what trains actually do and unpleasant acceleration I think. Your other argument is more important, it doesn't really matter for multi-hour trips
I mean, there's usually people running around in a train at any given moment, so I'm not sure there's technical considerations here so much as "we don't want people to stumble and fall" considerations :P
@Slereah which is probably one of the reasons why, where ACM is, the public transport is more adequate to the number of people and the buses are not that full
Theoretically a continuous system is made up of a continuously infinite number of particles and a continuous spectrum 'fock space' is able to handle that as bizarre as it is, it's just not clear that this needs to be excluded in general
I would buy that $(1, 1, 1, \ldots)$ isn't a real state since it's (maybe?) not with finite norm, but otoh the Fock space is in momentum basis so this makes everything harder to think about
@Slereah I mean, why would you know people who make jokes in German? You're not gonna get them anyway (either due to the language barrier or to due lacking the societal/political context)
@ACuriousMind Wait. I thought you need to include almost all forces involved. Since there is an applied force, I thought you also need to include the frictional force
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I wouldn't exactly call trains slow, some of them reach speeds of 300 km/h and higher - what exactly are you comparing them to when calling them "slow"?
then I still don't understand the question - if you're talking about the top speed, how could it possibly be the "slow acceleration" and not the low top speed that's the reason?
@Semiclassical is the reason you take the C (particle-antiparticle conjugate) to be the Hermitian conjugate because the annihilation operator is the is the Hermitian conjugate of the corresponding creation operator?
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