On the structure of quantum phase space

The space of labels characterizing the elements of Schwinger’s basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.