Homework 3

Q4 : a) Given a left-handed Weyl spinor ψ L ∈ (1/2, 0), show that σ 2 ψL ∗ is a righthanded
spinor. ( Here σ 2 is the usual second Pauli-matrix with purely imaginary entries.
b) Given a right-handed Weyl spinor ψ R ∈ (0, 1/2), show that σ 2 ψ ∗ R is a left-handed spinor.
( Here σ 2 is the usual second Pauli-matrix with purely imaginary entries.
c) Charge conjugation operation transforms a left-handed Weyl spinor into a right handed
one vice versa. Define charge conjugation on Weyl spinors as
ψ c L ≡ iσ 2 ψ ∗ L,
ψ c R ≡ −iσ 2 ψ ∗ R
Using these definitions, construct a bispinor , call it the Dirac spinor ψ D which satifies
(ψ c D) c = ψ D .
d) Again, using these definitions, construct a bispinor , call it the Majorana spinor ψ M
which satisfies ψ c M = ψ M .
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