SU(3) gauge field theory of spin-1 Bose-Einstein condensates

We reformulate hydrodynamic theory of spin-1 Bose-Einstein condensates (BEC) in terms of an SU(3) gauge field and describe the mean-field dynamics equivalent to the multicomponent Gross-Pitaevskii equations. In this theory, the spin vector and the nematic tensor constitute a single nine-component tensor which serves as an SU(3) gauge field and describes the spin-nematic texture in space and time. The constraints among the SU(3) gauge field imply the invariance of effective gauge potentials which encapsulate all effects of physical quantities and external fields. Compared with hydrodynamic theory, this new formulation greatly simplifies constraints on the gauge field and makes the derivation of hydrodynamic equations physically transparent.