Functional Quantum Theory of the Nonlinear Spinor Field as a Lepton-Hadron Model with Quark- Confinement

Functional quantum theory is a new formulation of quantum theory and a new field theoretic calculational procedure which allows the treatment of quantized fields with positive metric as well as with indefinite metric beyond perturbation theory. It was developed by Stumpf and coworkers, cf. Stumpf [1]. In particular, it was devoted to the evaluation of Heisenberg's quantized nonlinear spinor equation with dipole ghost regularization, cf. Heisenberg [2]. The basic idea of this approach is to regularize the non-renormalizable nonlinear spinor field by a combination of a real physical particle, a monopole ghost particle and a dipole ghost particle in the one-particle sector of the corresponding state space. This leads to an indefinite metric in this space. In order to achieve a correct physical and probabilistic interpretation of this regularization procedure, the ghost particles must have the following properties: