Conformally covariant coupled non-linear field theory on the hypercone: Vacuum solutions and quantization of normal modes

For the conformally covariant coupled non-linear spinor-scalar fields of the σ-model type we show that the non-trivial vacuum instanton solutions have a geometric meaning as constant spinors on the five-dimensional hypercone. The quantized fields around these solutions correspond to the normal modes of the hypercone. A connection is thus established between field theory, particle spectrum of the fields and quantized excitations of a geometry (the hypercone). (author)