Nuclear Physics and the non-relativistic conformal fixed point and all that!

Nuclear physics is sometimes considered to be a dead subject sometimes, by some people. I dont think that is the case. Its merely not fashionable for many people. And why not? Maybe it does not have high sounding terminology embedded in it. Anyway, in this entry I will try to argue that it is indeed interesting,--very interesting; and some very cool features can be seen in it. Since I am not a nuclear physicist, my description will be rudimentary.
Lets come to the concept of non-relativistic conformal field theories. Suppose you have a set of fermions interacting with each other. Then there is a phase shift associated with the incoming and outgoing fermion wavefunctions. Now imagine, that the interactions between the fermions can be tuned by tuning some coupling, say the magnetic field. For strong coupling, the fermions could be bound into fermions, while for arbitrary weak coupling they would form a Cooper-pair type bound state. The scattering length changes sign in these two phases, and at the point of transition it diverges, giving rise to universal physics. Thats the non-relativistic conformal fixed point I was referring to.
Now about the nuclear physics connection. The nucleon-nucleon (N-N) scattering length is of prime importance in nuclear physics. For real world, its small and negative for the pion phase shift in a particular channel. It is believed that tuning the quark mass would change the sign of the pion phase shift! The quark mass plays the role of the coupling in the previous example.
I am not yet aware of the implications of this interesting phenomena, but I do intend to find out.
True, I have glossed over the details, but I will add a more complete picture as and when I get it.

Ground and Scattering states

One of the things that I gained a bit more understanding of during the course of this Nuclear conference that is going on now is the issue of the scattering and bound states, which I am going to say here in a very hand-waving way.
The point is the issue that the S-matrix of a QFT that you calculate on the lattice is very different from the one that in continuum. For sure. But then, how can we get information about the continuum S-matrix. The seminal work of Luscher showed how this can be done. He argued this information lies in how the energy levels scale. If it is a bound state then there is scaling by exp(-m*L) where m is the mass of the bound state and L the lattice size. On the other hand, if it is a scattering state then it will scale by 1/L^3. Thus, a S-matrix with only poles gives the information about the full spectrum of the continuum theory with both the bound and scattering states. There's some bit about the momentum dependence of the phase shifts that come in somewhere, but I dont know that yet. Will hopefully learn that while doing this project with Nilmani, Anyi and Shailesh.

Another nice movie: Udaan. Watched it yesterday. Somehow it resonated with me for obious reasons. If only I could get free like that right now. But alas, no! Only an ominous patience for me.