Immersion Anomaly of Dirac Operator on Surface in R^3

Details Immersion Anomaly of Dirac Operator on Surface in R^3 Immersion Anomaly of Dirac Operator on Surface in R^3

1997-07-10

arxiv.org/abs/physics/9707010v1

Rev.Math.Phys. 11 (1999) 171-186

Physics

Mathematical Physics

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In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in $R^3$ 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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