General Relativistic Quantum Mechanics deriving Electroweak and Gravitational Interactions

TL;DR

This paper extends quantum mechanics with a general metric and invariance principles to derive a unified framework that reproduces electroweak interactions and Einstein gravity, proposing a novel gauge theory with an indefinite metric.

Contribution

It introduces a gauge theory with an indefinite metric and extended Lorentz symmetry to unify electroweak and gravitational interactions within a quantum framework.

Findings

Derived properties of the standard electroweak theory

Reproduced Einstein gravity from extended gauge symmetry

Proposed a chiral sextet model with enhanced Lorentz symmetry

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.