Homework 2

Question 1:
Verify that the Pauli matrices satisfy the identity σ_i σ_j = δ_ij + i ε_ijk σ_k,
and from it derive the commutation and anticommutation relations for these matrices.

Question 2:
Verify that the SU(2) matrix U₀(α,β,γ) is unitary and unimodular.

Question 3:
Which of these reactions is allowed, and which forces (strong, e.m., weak) govern the reactions?
(i) p + p—→ π⁺ + π^-
(ii) π⁰ → γ + γ
(iii) p + π⁰ → Δ⁺
(iv) K^- → π⁺ + π⁰
(v) Σ⁰ → Λ + π⁰
(vi) μ^- → e^- + ν—_e
(vii) n + n—→ π⁺ + π^- + π⁰
(viii) e⁺ + e^- → μ⁺ + μ^-
(ix) p → e⁺ + γ
(x) Σ⁺ → p + γ

Which conservation laws prevent the reactions which are not allowed?