Helfrich-Canham bending energy as a constrained non-linear sigma model

Details Helfrich-Canham bending energy as a constrained non-linear sigma model Helfrich-Canham bending energy as a constrained non-linear sigma model

2005-05-17

arxiv.org/abs/cond-mat/0505429v1

J.Phys. A38 (2005) 2593-2597

Physics

Condensed Matter

Soft Condensed Matter

5 pages

Scientific paper

10.1088/0305-4470/38/12/004

The Helfrich-Canham bending energy is identified with a non-linear sigma model for a unit vector. The identification, however, is dependent on one additional constraint: that the unit vector be constrained to lie orthogonal to the surface. The presence of this constraint adds a source to the divergence of the stress tensor for this vector so that it is not conserved. The stress tensor which is conserved is identified and its conservation shown to reproduce the correct shape equation.

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