Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 32D / a

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- Solution a

Solution

The transformations obey

g_{1}^{s} g_{1}^{r} = g_{1}^{s + r}

and

g_{1}^{0}

is the identity. If

x (t) = x (t) + s t

, then

d^{2} x / d t^{2} = d^{2} x / d t^{2}

. Thus solutions of the free-particle equation are mapped to solutions, so this is a one-parameter group of Lie symmetries.

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