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Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries outside the symmetry groups of the corresponding free equations. The Schrader construction of the so-called (relativistic) Maxwell group is reviewed through group extensions of kinematical groups associated with (constant and uniform) electromagnetic fields. The construction of the Galilean (nonrelativistic) Maxwell group is given.

This second part belongs to a series of two papers devoted to a constructive review of the relativistic wave equations for vector mesons due to the recent impact of spin one developments in connection with parasupersymmetric quantum mechanics. Here, the mesons are interacting with external (electro)magnetic fields but the simplest context of homogeneous constant magnetic fields directed along the z‐axis is particularly studied. Discussions on reality of energy eigenvalues, on causal propagation and on gyromagnetic ratios are especially presented. Supersymmetries and parasupersymmetries are analysed with respect to new pseudosupersymmetries suggested by these developments in one particular context.

This series of two papers is devoted to a constructive review of the relativistic wave equations for vector mesons due to the recent impact of spin one developments in connection with parasupersymmetric quantum mechanics. The free case as well as the interacting context with an electromagnetic field will be successively visited and discussed. Their associated parasupersymmetric properties will be pointed out. In this first part, the free context is presented by studying systematically the (symmetric) forms of wave equations subtended by a 16‐dimensional reducible representation of the Lie algebra sl (2, C) or, evidently, so (3, 1), this representation playing a well known role in p = 2‐parastatistical developments. Their hamiltonian forms are also discussed and some second order descriptions are finally reviewed.