QCD and hadronic matter under extreme conditions

This thesis is based on work done under the supervision of Dr. Stephen D. H. Hsu of Yale University and the University of Oregon. It is broken into three separate topics.;In chapter 2, we describe some detailed numerical simulations of Disoriented Chiral Condensates (DCCs), focusing on the possibility of multiple, independently coherent domains, and investigate the degree to which the DCC signal is attenuated. Though we found strong domain-domain interactions, we argue that viable signals exist for DCC detection. We briefly discuss some long-lived 'pseudo-bound state' configurations which arise at large field strengths.;In chapters 3 and 4, we explore this class of 'pseudo-bound states' (PBS). The configurations are long-lived, and could arise as remnants of a DCC. We show that the chiral Lagrangian equations of motion for a uniformly isospin-polarized domain reduce to those of the Sine-Gordon model. We investigate the possibility of PBS formation from multiple domains of DCC, and show that the probability of formation is non-negligible. Finally, we develop an algorithm which can exclude the existence of classical breathers (periodic finite energy solutions) in scalar field theories, and use it to show that PBSs are only approximately periodic and therefore quasi-stable.;In chapters 5 and 6, we derive an expression relating the superfluid gap and in-medium phase shifts in a system of non-relativistic fermions. Originally, we do so by applying effective field theory and renormalization group techniques to the problem of Cooper pair formation, thus arriving at a simple analytical expression for the 1S0 condensate which is free of nuclear potential model dependencies. The result is generalized for arbitrary angular momentum channels by solving the gap equation for the effective field theory description of excitations near the Fermi surface. We apply our results to the 1S0 and 3P2 condensates in neutron stars using phase shift data from scattering of free nucleons.