On the Orthogonality of Independently Propagating States as Occurring in the Lee-Oehme-Yang Theory

الأصل · EN

We generalize a theorem by Khalfin, originally derived for the states | F₁ > = | M⁰>, | F₂ > = | M⁰>, where M⁰ is a neutral flavoured meson (e.g., K⁰ or Bd⁰), by assuming CPT invariance. Dispensing with CPT invariance and allowing for an arbitrary pair of orthogonal states | F₁,₂>, we show that any linear combinations | Pₐ > = pₐ | F₁ > + qₐ | F₂> and | Pb > = pb | F₁ > - qb | F₂>, if postulated to be independently propagating in time, as in the Lee--Oehme--Yang Theory, must be mutually orthogonal. This implies a reciprocity relation: equality of the probabilities of the transitions | F₁ > ↔ | F₂>. Also implied is another relation involving the coefficients pₐ,b, qₐ,b, which can be interpreted as Im θ= 0, where θ is the rephasing-invariant parameter describing CPT violation in M⁰ M⁰ mixing for Khalfin's choice of | F₁,₂>. The states | F₁,₂> of our theorem need not form a particle-antiparticle pair, nor even be restricted to particle physics.