Quantum group based theory for antiferromagnetism and superconductivity: proof and further evidence

Previously one of us presented a conjecture to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of the critique by Baskaran and Anderson of Zhang's classical SO(5) model. This conjecture was further sharpened, experimental evidence and the important role of 1-d systems (stripes) was emphasized and moreover the relationship between quantum groups and strings via WZWN models were given in an earlier paper. In this brief note we give and discuss mathematical proof of this conjecture, which completes an important part of this idea, since previously an explicit simple mathematical proof was lacking. It is important to note that in terms of physics that the arbitrariness (freedom) of the d-wave factor g(2)(k) is tied to quantum group symmetry whereas in order to recover classical SO(5) one must set it to unity in an adhoc manner. We comment on the possible connection between this freedom and the pseudogap behaviour in the cuprates. (C) 2003 Elsevier B.V. All rights reserved.