Dirac operator on a conformal surface immersed in R-4: A way to further generalized Weierstrass equation

In the previous report (J. Ph3/a. A30 (1997) 4019-4029), I showed that the Dirac operator defined over a conformal surface immersed in R-3 by means of confinement procedure is identified with the differential operator of the generalized Weierstrass equation and the Lax operator of the modified Novik ov-Veselov (MNV) equation. In this article, using the same procedure, I det ermine the Dirac operator defined over a conformal surface immersed in R-4, which is for a Dirac field confined in the surface. Then it is reduced to the Lax operators of the nonlinear Schrodinger and the MNV equations by tak ing appropriate limits. It means that the Dirac operator is related to the further generalized Weierstrass equation for a surface in R-4.