A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture

In this short letter we review Schwinger’s formulation of Quantum Mechanics and we argue that the mathematical structure behind Schwinger’s “Symbolism of Atomic Measurements” is that of a groupoid. In this framework, both the Hilbert space (Schr"{o}dinger picture) and the $C^{\ast }$-algebra (Heisenberg picture) of the system turn out to be derived concepts, that is, they arise from the underlying groupoid structure.