Quantum dynamical manifolds. 4. High-temperature superconductors

A self-consistent, non-Abelian gauge theory is developed for high-temperatu re superconductors (HTSCs). As a physical example, a spontaneously broken ( SO(4) superset of SO(3) x U(1))(x3) gauge theory is described that includes excitonic and antiferromagnetic boson exchange pairing forces for the inte racting superconducting and antiferromagnetic phases of the soft supercondu ctor YBa2Cu3O7-x A new differential geometric approach for generating quant um dynamical manifolds, called quantum dynamical manifold theory (QDMT) is used to compute the quantum geometry of these systems. It is shown how geom etric conditions applied to the quasi-particle system can be used to determ ine self-consistent, self-gauge fields (SC-SGFs) and fix the coupling const ants to reduce the calculational number of degrees of freedom of such many- body systems. The resulting theory is formulated in a way that real crystal quasi-particle basis sets are used. This work raises the hope that ab init io property calculation and systematic exploration of different mechanisms for HTSCs will become possible. (C) 2000 John Wiley & Sons, Inc.