Immersion Anomaly of Dirac Operator on Surface in R^3
Mathematical Physics
2014-11-18 v1 math.MP
Abstract
In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward-Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface.
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Cite
@article{arxiv.physics/9707010,
title = {Immersion Anomaly of Dirac Operator on Surface in R^3},
author = {Shigeki Matsutani},
journal= {arXiv preprint arXiv:physics/9707010},
year = {2014}
}
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