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Diffeomorphism Invariant Formulation of CP Violation

Alibordi Muhammad

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.

Diffeomorphism Invariant Formulation of CP Violation

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.
Paper Structure (13 sections, 5 theorems, 41 equations)

This paper contains 13 sections, 5 theorems, 41 equations.

Table of Contents

  1. SM CPV Arises from Local Field Structures
  2. CP Violation in Curved Spacetime: Structural Failures
  3. Vacuum Uniqueness
  4. Structural Disintegration in Curved Spacetime
  5. Hadamard States and State-Dependent Mixing
  6. Diffeomorphism Invariant Reformulation
  7. Information-Geometric Formulation of CP Asymmetry
  8. Perturbative Structure of the Symmetric Denominator
  9. Antisymmetric Relative Entropy as Uhlmann Geometric Phase
  10. Diffeomorphism Invariance
  11. CP Conservation and Modular Thermal Equilibrium
  12. Summary
  13. Acknowledgment

Key Result

Proposition 3.1

For finite displacement from $\bm{\theta}$ to $\bm{\theta}'$ along a path $\mathcal{C}$ in the product manifold $\mathcal{M} \times \bar{\mathcal{M}}$:

Theorems & Definitions (10)

  • Proposition 3.1
  • proof
  • Theorem 3.2: Diffeomorphism invariance of information-geometric CP asymmetry
  • proof
  • Lemma 3.3
  • proof
  • Corollary 3.4: Foliation independence
  • proof
  • Theorem 3.5: Modular Thermal Equilibrium
  • proof