Some applications of mean field theory in strong-interaction physics

• Main Author: Barmore, Bryan Edward
• Format: Others
• Language: English
• Published: W&M ScholarWorks 1998
• Online Access: https://scholarworks.wm.edu/etd/1539623940; https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=3535&context=etd

Mean-field theory is a powerful tool that allows for significant insight into the very complicated problems of nuclear physics. By reformulating the many-body problem into a one-body, self-consistent system, much can be learned and explained.;In the framework of the sigma-omega model of the nucleus taken in relativistic mean-field theory, the radiation of vector mesons is studied. In the sigma-omega model there is a massive vector meson that couples to a conserved baryon current. During a relativistic heavy-ion collision, the nuclei (collections of baryons) undergo extreme deceleration. The vector mesons are radiated via a bremsstrahlung mechanism during the deceleration. We find a characteristic angular distribution for out-going energy of these mesons that is robust against variations in the three parameters in this model. Predictions for the total energy radiated suggests that a few percent of the total energy lost could be in this process.;Mean-field theory is also applied to calculations of the phase diagram in a U(1) lattice gauge theory. Variational mean-field theory along with gauge fixing allows for a precise description of the phase diagram above the phase transition. Below the transition point Pade approximants to the strong coupling expansion are used. Both analytic methods describe their respective phase through a metastable region seen in higher dimensions. In analogy to the Van der Waals' equation of state, the phase diagram near the transition point is described by a cubic function. This leads to an accurate determination of the transition point and a complete analytic description of the U(1) phase diagram. For comparison, Monte Carlo calculations are performed for se diagram. For comparison, Monte Carlo calculations are performed for dimensions 4--7.