Nuclear Physics Seminar

The study of QCD (Quantum Chromo-Dynamics) at low energies is relevant to explaining the sub-atomic world but is extremely difficult due to the mathematical structure of the theory. We use the O(4) linear sigma model with quark fields to study the chiral phase transition as a function of the temperature T and the baryon chemical potential μ_B . As an effective model for QCD, we hope to reproduce some aspects of the QCD phase diagram, namely, the line of first order phase transitions that has a critical endpoint at a second order phase transiton. We study how this line varies with changing pion mass. We use a fully self-consistent method which includes both mean fields and fluctuations. We study the mesonic and quark properties, including mean field, fluctuations and effective masses and how they relate to the transition structure.

It is well known that point transformations of a Lagrangian leave the Euler-Lagrange equations of motion unchanged. The question becomes much more difficult in the context of quantum field theory. It was first studied in the context of zero temperature field theory. It was shown that the S-matrix elements are independent of the choice of field appearing in the Lagrangian. This is equivalent to the statement that observables are invariant under a field redefinition for the fields appearing in the Lagrangian. This theorem holds for renormalizeable field theories. The case of finite temperature is much less understood. We study the difficulties of our self-consistent method in terms of field redefinitions.