Feynman's Propagator in Schwinger's picture of Quantum Mechanics
| Autor: | Ciaglia, Florio M., Di Cosmo, Fabio, Ibort, Alberto, Marmo, Giuseppe, Schiavone, Luca, Zampini, Alessandro |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Modern Physics Letters, 36 (26) 2150187 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S021773232150187X |
| Popis: | 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 $L$. Comment: 16 pages |
| Databáze: | arXiv |
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