 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2014/paper-1/4/a/solution

(+, -, -, -)

and units

ℏ = c = 1

. Varying

ϕ^{*}

and

ϕ

independently gives

(□ + m^{2}) ϕ = 0, (□ + m^{2}) ϕ^{*} = 0.

In the divergence of the stated current, the products of first derivatives cancel, leaving

\partial_{μ} j^{μ} = i q (ϕ^{*} □ ϕ - ϕ □ ϕ^{*}) = 0.

The two identical mass terms cancel on the field equations.

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