General Relativistic Quantum Mechanics deriving Electroweak and Gravitational Interactions

TL;DR

This work proposes a generalization of quantum mechanics by introducing an indefinite inner-product metric $\xi$ and requiring invariance under general linear transformations, enabling Lorentz symmetry to inhabit the gauge space and enabling a unified treatment of spacetime and gauge symmetries. By employing a spontaneous fusion mechanism of overlapping Lorentz symmetries within a chiral sextet of leptons, the authors derive an electroweak-like theory and, under curvature, gravitational interactions, predicting relations such as $\sin^2\theta_W=1/4$, $m_H=\sqrt{2}\,m_Z$, and $\lambda=g_W^2/3$, with right-handed leptons and gravity emerging from the same multiplet structure. The formalism achieves probability positivity through second quantization and gauge-invariant constructions, while acknowledging scale tensions between the electroweak and gravitational sectors and outlining a path toward an electroweak–gravity unification via Lorentz symmetry fusion. Overall, it presents a novel route to unification by treating Lorentz symmetry as a gauge degree of freedom and fusing it with spacetime symmetry to reproduce known interactions and predict testable relations. These ideas point toward a framework in which Lorentz and gauge structures are intertwined at a fundamental level, potentially informing approaches to quantum gravity and beyond-Standard-Model unification.

Abstract

A gauge theory with an indefinite metric without negative probabilities is given by extending quantum mechanics, where a general metric is introduced, and the invariance under the general linear transformation is imposed on the space of quantum states. On this basis, we construct and investigate a chiral sextet model, which has one more Lorentz symmetry in the gauge space, to derive much properties of the standard electroweak theory, and also Einstein gravity, when the double Lorentz symmetry spontaneously fuses into one.