Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 15.6.3

Testing the Quark Model — Robert Mann

Physics — Particle Physics · g-parity

Problem

Consider the operator G=Cexp⁡(iπI2)\mathbb{G} = \mathbb{C} \exp\left(i\pi \mathfrak{I}_2\right) an operator known as the G\mathbb{G}-parity operator, where C\mathbb{C} is the charge-conjugation operator and I2\mathfrak{I}_2 is the 2nd component of the isospin operator I⃗\vec{\mathfrak{I}}. (a) Suppose we define for the pion C∣π±⟩=−∣π∓⟩\mathbb{C}\left|\pi^{\pm}\right\rangle = -\left|\pi^{\mp}\right\rangle Show that under G\mathbb{G}-parity G∣π⟩=−∣π⟩\mathbb{G}\left|\pi\right\rangle = -\left|\pi\right\rangle for the pion triplet. (b) What is the action of G\mathbb{G} on a state ∣Ψ(nπ)⟩|\Psi(n\pi)\rangle of nn pions?

Browse the problem library