Periodic boundary conditions allow you to calculate properties for infinite systems which is more appropriate than just making a large box. This is the basis for the band theory of solids.
Donaresh,
From experience, the most important finite group with which you will want to deal with in physics is the symmetric group. Fortunately this group has a lot of exactly known properties and derived results. You could try
Fulton. Young tableau, representation theory and geometry...
An understanding of the histoy of physics is critical for a complete understanding of how the physical universe is quantitatively described. I just don't think you will find many physicists admitting as such. All the nomeclature is borrowed from earlier paradigms and can give insight into how...
The Pauli exclusion principle is phenomenoligical. However the mathematics behind such mechanisms is well understood in that if we say
'If a type of particle has the propertu that only one particle is able to any particular state'
then we can go quite a long way. However no one really...
The gold foil was pretty thin, but the point of the experiment was that if the 'size' of nuclei were what they were supposed, the scattering angle would have been much larger. Instead of you hand let's talk about making the gold thicker and thicker. Forget all that crap about tunnelling through...
What? This is not the Hamiltonian for special relativity? A can't even be bothered explaining why it isn't, but just think about how we would go about quantising this.
Then how do you explain Rutherfords experiment where he was able to shoot helium through a sheet of gold. QM definitely tells us that what was previously thought as solid i.e. a smooth rigid continuum is not entirely true. In fact, QM can show us that our previous notion of the phases of matter...
Are you really sure you want to say 'mathematically well defined'. Dyson has shown that the perturbation series is most probably divergent. And I have not met a mathematician yet who says that renormalisation is mathematically well defined.
Well I know that this is definitely not correct.
You will get onto coupling electromagnetism with the dirac equation soon, hopefully showing how it comes about through gauge invariance. In this instance, the strength of the coupling is related to charge, e. The problem of having a gauge invariant theory for gravitation, where the coupling...
Strangely enough, Goldsteins book on classical mechanics contains a lagrangian formulation of the Schrodinger field. As was said it can be very useful, especially if you dislike the use of creation and annihilation operators.
I especially refer to the 'There has to be messengers'. In what sense does they have to exist. They are certainly never detected. Classical physics does not require quantised fields for charges to interact via a finite propagation speed of the interaction. Look at GR.
Can you please give me an example of the 'time reparametrisation' you are talking about? I want to make sure that we are actually discussing is the same thing and if you are correct:smile:
Sorry? Has everybody gone mad?
If you have invariance under reparemtrisations then you gave gauge degress of freedom that have to be fixed. Take the example of the E.M. Field. Integrate the lagrangian by parts, set surface terms to zero to get the lagrangian density L=AG^-1A where G^-1 is the...