[LECS/CM-04002]

The Hamiltonian of a charged particle in electromagnetic field is derived starting from the Lagrangian.

The Hamiltonian  for a charged particle in electromagnetic field is invariant under the gauge transformation \[\vec A \longrightarrow \vec A^\prime = \vec A -\nabla \Lambda\]if the canonical momentum is taken to transform as \[\vec p \longrightarrow \vec p^\prime -(e/c) \nabla \Lambda.\]