I have recently been to a guest lecture about low energy QCD with a finite isospin chemical potential. I have two overall questions about this, since it wasn’t possible to ask questions at the given lecture, and i have to wait a while before future classes about this are available.
Question 1: It was mentioned that in low energy QCD the baryon chemical potential has no effect in chiral perturbation theory. Can anyone briefly explain why this is so?
Question 2: In general i would like to know how the isospin chemical potential enters the effective QCD Lagrangian, and what kind of changes it brings - i.e. what it actually does. We can just take the simpler case where the baryon chemical potential is set to zero: $\mu_B = 0$
I know it has something to do with promoting $SU(2)_L \times SU(2)_R$ to a local gauge symmetry, and that $\mu_I$ will enter the chiral Lagrangian through the covariant derivative as a zeroth component of a gauge potential. How can one see this?
I would be very interested in literature which can give me an introduction to isospin chemical potential in effective low energy QCD Lagrangians - especially with the connection to the chiral condensate and isospin density. But as far as this question goes, the focus is just to start with understanding the chemical potentials of QCD. I have spent a couple of hours reading everything i could find both on stackexchange and in various published papers. With this question, I am trying to boil everything down to a basic understanding.
Thank you very much.