Pseudo-Conformal Field Theory

Abstract Starting from the observation that the 2-d Polyakov action is metric independent without being topological, while the 4-d Weyl-conformal action is not metric independent, I searched for a 4-d structure and field equation which would be metric independent. I found that the structure is the existence of a geodetic and shear-free Newman-Penrose (NP) null tetrad, which is a Frobenius integrable structure, called lorentzian Cauchy-Riemann (LCR) structure. The metric independent equation is a gauge field equation identified with the gluon field. Imposing the LCR-structure as the fundamental structure of nature (instead of the Einstein-metric) all the interactions (gravity, electroweak and gluonic) are derived. The three generations of the leptons are solitonic configurations with precise topological invariants. The quarks are confined sources of the gluonic field implied by the LCR-tetrad of the corresponding leptons. Quantum field theory emerges through the Bogoliubov causal approach and the standard model is derived through the Scharf procedure of the Kugo-Ojima BRS elimination technique of the unphysical modes of the spin-1 and spin-2 fields.