Gauge-independent minimal electromagnetic coupling

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Abstract
The interaction of the electromagnetic field with charged particles is frequently described by a quasi-invariant Lagrangian and consequently by a Hamiltonian that is gauge dependent. A systematic procedure is given for obtaining a gauge-independent Lagrangian and hence a gauge-independent Hamiltonian. The analysis which is mainly concerned with nonrelativistic charged particles in external electromagnetic fields is similar to Mandelstam's gauge-independent and path-dependent quantum field theory.