Nonlinear spinor theory in de Sitter space

Abstract

The nonlinear spinor equation is formulated in a de Sitter space with symmetry groupSO1,4. The curvature of space-time introduces an absolute scale of lengthR which leads to a breakdown of dilatation invariance. If this radiusR is postulated to be the only scale of length in the theory noncanonical quantization seems unavoidable. In particular, a quantization procedure is discussed, which introduces the fundamental lengthR into the theory, even at very small space-time distances, near the light cone. As a further point the definition of a parity operation in nonlinear spinor theory is suggested, using the discrete transformation connecting antipodal points in de Sitter space.