In the coherency-matrix formalism (CMF), the state of polarization of the field as well as the physical devices are represented in terms of 2×2 matrixes. The possibility of being able to exchange the role played by these matrices in the CMF is considered and a versatile operator formalism is developed. The physical meaning of the various operator relations is given and the possibility of obtaining the form of the most general operator that commutes with a given physical device is discussed. The operator formalism is applied to the study of certain physical devices whose matrix operator representations have been constructed through the use of Pauli spin matrices. Emphasis is placed on the identification of all the operators (including the Pauli spin matrices) in terms of combinations of known physical devices. In this way, the physical meanings of the various operator relations are discussed together with the meanings of the commutation relations between the various well-known physical devices. Finally, the forms of the most general operators that commute with the respective operators considered in this paper are obtained.
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