We find out that both the matrix and the operator CPT groups for the spin-3/2 field (with or without mass) are respectively isomorphic to D 4 Z 2 and Q × Z 2 . These groups are exactly the same groups as for the Dirac field, though there is no a priori reason why they should coincide.

We show that the CPT group of the Dirac field emerges naturally from the PT and P (or T) subgroups of the Lorentz group.Comment: 4 pages, no figure

Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the deformation quantization formalism, in relation to the Dirac field case. This happens because the vector structure of the RS field imposes constraints on the space of wave function solutions and not on the operator structure. The RS propagator was also calculated within this formalism.

We show that the CPT groups of QED emerge naturally from the PT and P (or T ) subgroups of the Lorentz group. We also find relationships between these discrete groups and continuous groups, like the connected Lorentz and Poincaré groups and their universal coverings.

Even if at the level of the non-relativistic limit of full QED, C is not a symmetry, the limit of this operation does exist for the particular case when the electromagnetic field is considered a classical external object coupled to the Dirac field. This result extends the one obtained when fermions are described by the Schrödinger-Pauli equation. We give the expressions for both the C matrix and theĈ operator for galilean electrons and positrons interacting with the external electromagnetic field. The result is relevant in relation to recent experiments with antihydrogen.