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arXiv · 1001.1183

Spinor representation of surfaces and complex stresses on membranes and interfaces

Jemal Guven·Pablo Vázquez-Montejo
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Abstract

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.

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Jemal Guven, Pablo Vázquez-Montejo. 2010-01-08. Spinor representation of surfaces and complex stresses on membranes and interfaces. https://doi.org/10.1103/physreve.82.041604

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