 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-305/1/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

t_{0} = 1

and

t_{i} = - 1

for spatial indices. The complex conjugation of the scalar

i

supplies a minus sign, while conjugating each of the three spatial gamma matrices supplies three more. In the original order,

B^{- 1} γ^{5 *} B = - i (B^{- 1} γ^{0 *} B) (B^{- 1} γ^{1 *} B) (B^{- 1} γ^{2 *} B) (B^{- 1} γ^{3 *} B) = (- i) (- 1)^{3} γ^{0} γ^{1} γ^{2} γ^{3} .

Consequently the chirality matrix obeys

B^{- 1} γ^{5 *} B = γ^{5} .

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