Standard Model Derivation from a 4-d Pseudo-Conformal Field Theory

TL;DR

This paper derives the Standard Model from a 4-dimensional pseudo-conformal field theory based on Lorentzian Cauchy-Riemann structures, providing a geometric foundation for particles and interactions.

Contribution

It introduces a novel geometric framework using LCR-structures to derive the Standard Model, including particles, potentials, and interactions, from a pseudo-conformal field theory.

Findings

Derivation of the Standard Model Lagrangian from PCFT.

Identification of electron and neutrino as specific LCR-manifolds.

Explicit gravitational and electroweak potentials for particles.

Abstract

Pseudo-conformal field theory (PCFT) is a 4-d action, which depends on the lorentzian Cauchy-Riemann (LCR) structure, determined by a tetrad satisfying precise integrability conditions. This LCR-tetrad defines a class of Einstein metrics and an electroweak U(2) connection. A static massive and a massless LCR-manifolds are found. The massive soliton is compatible with the Kerr-Newman manifold. Its two conjugate LCR-structures have g=2 gyromagnetic ratio and opposite charges, suggesting their identification with the electron and positron particles with a naked ring essential singularity. Their background CP(3) formulation bypasses the Hawking-Penrose singularity theorems. The massless LCR-manifold does not have a charge, suggesting its identification with the neutrino. The LCR-structure formalism provides the particles separated into left and right handed chiral parts, the left and right columns of the homogeneous coordinates of the grassmannian G(4,2). The electron LCR-tetrad explicitly provides its gravitational and electroweak potentials (dressings). Their distributional nature permit us to use the Bogoliubov causal perturbative approach (improved by Epstein-Glaser and Scharf et. al. techniques) as a pure mathematical harmonic expansion in the Gelfand rigged Hilbert-Fock space of tempered distributions of the Poincare representations (corresponding free fields). This S-matrix computational procedure in the proper Gelfand triplet, provides the standard model lagrangian for the electromagnetic, weak and Higgs interactions. The interacting terms and the relation between the masses and the coupling constants are implied by the Scharf et. al. operational algorithm on the free fields. In PCFT the computed gluon potential (static quark dressing) cannot be treated with the Bogoliubov procedure. Possible solutions of the dark matter and neutrino mixing problems are discussed.