 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2017/8/a/i/solution

Use the four-momentum convention

p^{μ} = (E / c, p)

, with Minkowski signature

(+, -, -, -)

. For a particle of rest mass

m > 0

and three-velocity

v

p^{μ} = mγ (c, v), γ = \frac{1}{1 - ∣ v ∣ ^{2} / c ^{2}} .

Here

E = γm c^{2}

and

p = γm v

, so

p^{μ} p_{μ} = m^{2} c^{2}

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