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arXiv · 2109.05756

Feynman's Propagator in Schwinger's picture of Quantum Mechanics

Florio M. Ciaglia·Fabio Di Cosmo·Alberto Ibort·Giuseppe Marmo·Luca Schiavone·Alessandro Zampini
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Abstract

A novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac-Feynman-Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function $\ell$ on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian $\ell$ allow to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman's original derivation of the propagator for a point particle described by a classical Lagrangian $L$.

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Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone, Alessandro Zampini. 2021-09-13. Feynman's Propagator in Schwinger's picture of Quantum Mechanics. https://doi.org/10.1142/s021773232150187x

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