Diffeomorphism Invariant Formulation of CP Violation

TL;DR

This paper explores the conflict between standard CP violation descriptions and diffeomorphism invariance in general relativity, proposing an information-geometric approach to reconcile these concepts.

Contribution

It introduces an information-geometric framework based on relative entropy to address CP violation within a diffeomorphism-invariant context.

Findings

Identifies tension between CP violation and general covariance.

Proposes an information-geometric approach using quantum states.

Suggests reinterpretation of Sakharov conditions in geometric terms.

Abstract

We identify a fundamental tension between the standard formulation of CP violation and diffeomorphism invariance in general relativity. The effective Hamiltonian approach, while phenomenologically successful, relies on a preferred time foliation that is incompatible with general covariance. The CP-violating phases are scalars along the worldline of the decaying parent particle; however, the definition of masses and phases presupposes a local covariant structure, which becomes ill-defined near the origin where curvature is large and metric fluctuations become significant. We propose an information-geometric framework based on relative entropy, exploiting pure quantum states in particle and antiparticle Hilbert spaces. We show how the Sakharov conditions could be reinterpreted in terms of information-geometric quantities, although a fully rigorous phenomenological implementation remains to be developed.