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Relativistic charged-particle action

Under $A_\mu\mapsto A_\mu+\partial_\mu\chi$, the interaction changes by
$$
q\int\frac{d\chi(x(\lambda))}{d\lambda}\,d\lambda
=q\,[\chi]_{\rm endpoints}.
$$
Fixed-endpoint equations of motion are therefore gauge invariant.


Gauge invariance of the charged-particle worldline action

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 37D / i / Solution

Gauge invariance of the charged-particle worldline action

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Gauge invariance of the charged-particle worldline action

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