The choice of the symmetry group for the cuprates

Abstract

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we discuss in the present note the choice of the classical symmetry group underlying the quantum group. Keeping in mind the degrees of freedom arising from spin, charge, and lattice we choose the classical group as SO(7). This choice is also motivated to accomodate the several competing phases which are or may be present in these and related materials, such as stripe phase [mesoscopically ordered phase], Luttinger liquids, nearly antiferromagnetic Fermi liquids, charge-ordered Fermi liquids, glassy phase, stringy phase and perhaps more. The existence and the behavior of pseudo-gap and lattice distortion are also an important consideration. We have lumped the charge, spin and lattice-distortion ordering and other orderings into the psuedogap.