Department of Physics,

Institute for Theoretical Physics,

Technical University of Clausthal,

Leibnizstr. 10,

38678 Clausthal-Zellerfeld, GERMANY

E-mail: asi@pt.tu-clausthal.de

and
*Renat ZHDANOV*

Department of Applied Research,

Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv-4, UKRAINE

E-mail: renat@imath.kiev.ua

**Nonlinear Dirac equations through nonlinear gauge tranformations**

**Abstract:**

A method proposed by H.D.D and G. A. Goldin to derive from a linear
Schrodinger equation a nonlinear extension through a group of physically
motivated nonlinear transformations (nonlinear gauge group) is generalised
to the Dirac equation. The nonlinear transformations N on the corresponding
Hilbert space are assumed to be local, separable (in connection with a
tensor product Hilbert space) and Poincare invariant. Furthermore N is
choosen such that the positional density is invariant. This group yields
a family F of nonlinear Dirac equations, which represents a nonlinear symmetry
of F and which describes systems physical equivalent to the linear Dirac
system. If one breaks this symmetry partly, e.g. if one changes the coefficients
and the functions which label N, one finds physically inequivalent i.e.
'new' nonlinear Dirac equations which are physically motivated as building
blicks in a framework of a nonlinear extension of a quantum theory which
could be interesting in the future.