SURFACES OBTAINED FROM ℂPN-1 SIGMA MODELS

In this paper, the Weierstrass technique for harmonic maps S2 → ℂPN-1 is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the ℂPN-1 model equations are defined on the sphere S2 and the associated action functional of this model is finite, then the generalized Weierstrass formula for immersion describes conformally parametrized surfaces in the su (N) algebra. In particular, for any holomorphic or antiholomorphic solution of this model the associated surface can be expressed in terms of an orthogonal projector of rank (N - 1). The implementation of this method is presented for two-dimensional conformally parametrized surfaces immersed in the su (3) algebra. The usefulness of the proposed approach is illustrated with examples, including the dilation-invariant meron-type solutions and the Veronese solutions for the ℂP2 model. Depending on the location of the critical points (zeros and poles) of the first fundamental form associated with the meron solution, it is shown that the associated surfaces are semiinfinite cylinders. It is also demonstrated that surfaces related to holomorphic and mixed Veronese solutions are immersed in ℝ8 and ℝ3, respectively.

QUANTUM MECHANICS ON Sn AND MERON SOLUTION

A particle in quantum mechanics on manifolds couples to the induced topological gauge field that characterizes the possible inequivalent quantizations. For instance, the gauge potential induced on S2 is that of a magnetic monopole located at the center of S2. We find that the gauge potential induced on S3(S2n+ 1) is that of a meron (generalized meron) also sitting at the center of S3(S2n+ 1).

Meron Pseudospin Solutions in Quantum Hall Systems

In this paper we report calculations of some pseudospin textures for bilayer quantum hall systems with filling factor ν=1. The textures we study are isolated single meron solutions. Meron solutions have already been studied at great length by others by minimising the microscopic Hamiltonian between microscopic trial wavefunctions. Our approach is somewhat different. We calculate them by numerically solving the nonlinear integro-differential equations arising from extremisation of the effective action for pseudospin textures. Our results can be viewed as augmenting earlier results and providing a basis for comparison. Our differential equation approach also allow us to dilineate the impact of different physical effects like the pseudospin stiffness and the capacitance energy on the meron solution.

Geometry of the SU (2) Di-Meron Solution

The geometric properties of the di-m eron solution to the SU (2) Yang-Mills equations are studied in detail. The essential geometric structure of this solution is that of a locally symmetric space endowed with a Riemannian structure which is conformally flat. The di-meron solution is representable by an integrable 3-distribution over Euclidean 4-space. The corresponding integral surfaces are obtained in analytic form.