Minimal electromagnetic coupling schemes. I. Symmetries of potentials and gauge transformations

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Abstract
Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries inside and outside the symmetry groups of the corresponding free equations. Subsymmetries of relativistic potentials are classified up to conjugacy under the kinematical groups of the associated (constant and uniform) electromagnetic fields. Through invariance conditions on (physical) four-potentials a maximal character of the symmetry is obtained leading to the maximal symmetry groups of the corresponding wave equations with interaction. Usual and compensating gauge transformations are analyzed within the context of such invariance conditions applied to arbitrary electromagnetic fields.