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arXiv · 1807.00519

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

Florio M. Ciaglia·Alberto Ibort·Giuseppe Marmo
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Abstract

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 (Schrödinger picture) and the $C^{*}$-algebra (Heisenberg picture) of the system turn out to be derived concepts, that is, they arise from the underlying groupoid structure.

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Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo. 2018-07-02. A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture. https://doi.org/10.1142/s0217732318501225

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