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• The topological nature of the Mott-Hubbard state is treated. • Landau-type quantization in the gauge field is considered. • An effective two-band model describing doped topological systems is formulated. The topological nature of the Mott-Hubbard state in strongly correlated systems is treated. These systems are described in terms of spin-charge separation, i.e. spinon-holon deconfinement in the gauge field. Analogies with the quantum Hall effect and Landau quantization are considered, the presence of the Chern-Simons term being important for proper description of the Hubbard splitting. Occurrence of topological frustrations with doping in an effective two-band model is demonstrated. The role of orbital degrees of freedom and possible occurrence of orbital currents are discussed. [ABSTRACT FROM AUTHOR]

Abstract The (2 + 1) -dimensional Maxwell–Chern–Simons gauge model consisting of two complex scalar fields interacting through a common Abelian gauge field is considered. It is shown that the model has a solution that describes a soliton system consisting of vortex and Q-ball constituents. This two-dimensional soliton system possesses a quantized magnetic flux and a quantized electric charge. Moreover, the soliton system has a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of a vortex and a Q-ball. [ABSTRACT FROM AUTHOR]

Abstract: On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. A structure of rotation symmetry is equipped with a Lagrangian including vorticity, in addition to Lagrangians of translation symmetry. From the action principle, Euler’s equation of motion is derived. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate . It is shown that, with the translation symmetry alone, there is freedom in the transformation between the Lagrangian -space and Eulerian -space. The Lagrangian provides non-trivial topology of vorticity field and yields a source term of the helicity. The vorticity equation is derived as an equation of the gauge field. The present formulation provides a basis on which the transformation between the space and the space is determined uniquely. [Copyright &y& Elsevier]