Quantum antiferromagnets and high temperature superconductivity

The problem of accurately calculating the various properties of high temperature superconductors remains one of the chief issues in theoretical condensed matter physics. In my thesis, I attempt to extend and refine certain aspects of a computational technique which is based on the gauge theory of the t-J Hamiltonian. I argue that the mean field solution used in previous work is inadequate for describing high temperature superconductivity, although it is not entirely inappropriate for describing certain gross properties of the high-{dollar}Tsb{lcub}c{rcub}{dollar} materials. The zero temperature magnetic properties of the t-J model, computed at the mean field level and modified with a crude vertex correction, agree quantitatively with those found in exact diagonalizations. A comparison with experimental results, however, reveals the specific nature of the deficiencies of the gauge theory approach. I claim that there are two modifications which, when made, rectify most of the shortcomings of this approach. The first is to consider the tendency toward phase separation in the t-J model and its manifestation in the behavior of the gauge field variables. The second is to address the issue of time reversal symmetry breaking, the lack of evidence for which has been construed as a major, if not fatal, drawback of the calculational technique. I conclude by suggesting a course of action which, if taken, should help to clean up the mess in the gauge theory of the t-J model and reconcile several of the existing theories of high temperature superconductivity.