Ghost-free Formulation of Quantum Gauge Theory on Fractal Spacetime

Abstract

It is known that quantization of massless spin-1 particles runs into several related complications such as the redundancy of gauge orbits, the presence of extra degrees of freedom and the need to introduce “ghost” fields. The textbook interpretation of quantum gauge theory is that “ghosts” are unphysical objects whose function is to preserve Lorentz covariance and unitarity.  In particular, Faddeev-Popov “ghosts” (FPG) violate the spin-statistics theorem and are devoid of measurable properties. FPG are shown to decouple from the spectrum of observable states, yet it remains unclear how their presence in loop diagrams and their interaction with gauge fields is even possible in the absence of any physical attributes. The object of this work is to suggest that, at least in principle, the concept of spacetime endowed with minimal fractality enables a “ghost”-free formulation of quantum gauge theory. Our approach opens the door for a non-perturbative understanding of vacuum polarization in Quantum Electrodynamics (QED).