Improved Lee, Oehme and Yang approximation

TL;DR

This paper identifies and corrects inconsistencies in the standard LOY approximation for effective Hamiltonians in two-state quantum systems, providing improved formulas that respect CPT symmetry and extend to three-state systems.

Contribution

It introduces corrected and improved formulas for the effective Hamiltonian in two and three state subspaces, addressing previous inconsistencies in the LOY approximation.

Findings

Corrected formulas for H(eff) that respect CPT symmetry.

Inconsistencies in standard LOY assumptions are identified and addressed.

Extended formulas for three-state subspaces are derived.

Abstract

The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in assumptions and approximations used in the standard derivation of the LOY effective Hamiltonian, H(LOY), governig this time evolution are found. Eliminating these inconsistecies and using the LOY method, approximate formulae for the effective Hamiltonian, H(eff), governing the time evolution in this subspace (improving those obtained by LOY) are derived. It is found, in contradistinction to the standard LOY result, that in the case of neutral kaons (<K(0)|H(eff)|K(0)> - <K(0)-bar|H(eff)|K(0)-bar>), cannot take the zero value if the total system the preserves CPT--symmetry. Within the use of the method mentioned above formulae for H(eff) acting in the three state (three dimensional) subspace of states are also found.