Tetrads in low-energy weak interactions
Alcides Garat
TL;DR
The paper proposes a geometrical framework in which low-energy weak-interaction processes are analyzed by assigning locally defined tetrads to spacetime points at interaction vertices. Using Abelian and non-Abelian constructions, it introduces duality rotations and complexions ($\alpha,\beta,\vartheta$) to generate extremal fields that diagonalize stress-energy and produce orthogonal tetrad blades, with local gauge transformations ($U(1)$, $SU(2)$) mapped to boosts and rotations on these blades. It then applies this formalism to explicit processes like inverse muon decay and elastic neutrino–electron scattering, showing that vertex tetrads are related by local $SU(2)$ tetrad gauge transformations while the spacetime metric remains invariant, effectively linking standard gauge states to spacetime geometry. The work argues for a deeper link between gauge theories and gravitational-like tetrad structures, discusses extensions to higher-order diagrams and curved spacetimes, and outlines open questions about gauge gravity and potential connections to the Higgs mechanism and symmetry breaking. Overall, the approach provides a novel, geometry-centered perspective on perturbative weak interactions with potential implications for unifying spacetime geometry and quantum field theory.
Abstract
Tetrads are introduced in order to study the relationship between tetrad gauge states of spacetime and particle interactions, specially in weak processes at low energy. Through several examples like inverse Muon decay, elastic Neutrino-Electron scattering, it is explicitly shown how to assign to each vertex of the corresponding low-order Feynman diagram in a weak interaction, a particular set of tetrad vectors. The relationship between the tetrads associated to different vertices is exhibited explicitly to be generated by a SU(2) local tetrad gauge transformation. We are establishing a direct link between standard gauge and tetrad gauge states of spacetime using the quantum field theories perturbative formulations.