Non-Abelian gauge theories : analogies in condensed matter systems

Abstract

The work in this thesis is written with the following question in mind: does the physics investigated in colliders like the one at CERN have its counterpart in phenomena like superfluidity and superconductivity? More precisely, this thesis focuses on the condensed matter parallel of non-Abelian gauge theories exploited in high-energy physics. These theories capture the notion of parallel transport and offer the possibility of deconfinement, i.e., the existence of quarks and gluons. In the first part of the thesis, the notion of parallel transport in the context of spin-orbit coupled systems is studied, which have attracted much attention in recent years. The question arises whether hydrodynamic conservation laws for non-Abelian spin currents exist. The answer is yes, provided the spin system is in a superfluid state. In the second part, the doped Mott insulator is studied, which is relevant for the problem of high-temperature superconductivity. A gauge theory considering the electron as being split up into spinons and holons (a condensed matter analogue of quarks and gluons) is studied. It is shown how this theory, when some subtle issues are treated correctly, leads to physical predictions which can be (and, in some cases, have been) confirmed experimentally.