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Theoretical Physics course of the University of Cambridge

Theoretical Physics I course of the University of Cambridge

Past exam of the theoretical physics I course of the University of Cambridge

2014

Paper 1

Use metric signature $(+,-,-,-)$ and units $\hbar=c=1$. Varying $\phi^*$ and $\phi$ independently gives
$$
\boxed{(\Box+m^2)\phi=0,\qquad(\Box+m^2)\phi^*=0.}
$$
In the divergence of the stated current, the products of first derivatives cancel, leaving
$$
\partial_\mu j^\mu=iq(\phi^*\Box\phi-\phi\Box\phi^*)=0.
$$
The two identical <mass> terms cancel on the field equations.

Solution

Past exam of the theoretical physics I course of the University of Cambridge / 2014 / Paper 1 / 4 / a / Solution

Past exam of the theoretical physics I course of the University of Cambridge / 2014 / Paper 1 / 4 / a / Solution

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