What question did this study set out to answer?

The aim is to extend the Information Geometry Unification Principle (IGUP) to incorporate internal gauge symmetries.

March 31, 2026Open Access

Information Geometry Unification Principle II

Puntos clave

The aim is to extend the Information Geometry Unification Principle (IGUP) to incorporate internal gauge symmetries.
Constructed principal fiber bundles over the quantum information manifold.
Defined gauge potentials as affine connections.
Derived field strengths as bundle curvatures in detail.
Formulated the Yang–Mills Lagrangian as a geometric invariant of IGUP.
Unified gauge groups $U(1)$, $SU(2)$, $SU(3)$ within the information geometry framework.
Demonstrated that the Yang–Mills Lagrangian is a natural geometric invariant.
Unified gravity, quantum theory, and the Standard Model through a full Lagrangian representation.
Provided explicit and self-contained derivations throughout the paper.

Resumen

This paper extends IGUP to include internal gauge symmetries. We construct principal fiber bundles over the quantum information manifold M. We define gauge potentials as affine connections, derive field strengths as bundle curvatures in full component detail, and show that the Yang–Mills Lagrangian is a natural geometric invariant of IGUP. We unify U (1), SU (2), SU (3) within the information geometry framework, and write the full Lagrangian unifying gravity, quantum theory, and the Standard Model. All derivations are explicit and self-contained.

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