Complexity in quantum field theory and physics beyond the standard model

Complex quantum field theory (abbreviated c-QFT) is introduced in this paper as an alternative framework for the description of physics beyond the energy range of the standard model. The mathematics of c-QFT is based on fractal differential operators that generalize the momentum operators of conventional quantum field theory (QFT). The underlying premise of our approach is that c-QFT contains the right analytical tools for dealing with the asymptotic regime of QFT. Canonical quantization of c-QFT leads to the following findings: (i) the Fock space of c-QFT includes fractional numbers of particles and antiparticles per state, (ii) c-QFT represents a generalization of topological field theory and (iii) classical limit of c-QFT is equivalent to field theory in curved space–time. The first finding provides a field-theoretic motivation for the transfinite discretization approach of El-Naschie’s ε(∞) theory. The second and third findings suggest the dynamic unification of boson and fermion fields as particles with fractional spin, as well as the close connection between spin and space-time topology beyond the conventional physics of the standard model.