Summary
We discuss some geometric aspects of the Feynman path integral approach for a nonrelativistic Hamiltonian system. Path integrals are considered for the case in which the underlying manifold is multiply connected and the contributions of different homotopy classes of paths are analysed by using covering spaces. Finally, we investigate path integrals for identical particles.
Riassunto
Si discutono alcuni aspetti geometrici dell’approccio all’integrale del percorso di Feynman per un sistema hamiltoniano non relativistico. Si considerano gli integrali di percorso per il caso in cui la molteplicità sottostante è molteplicemente connessa e si analizzano i contributi di diverse classi di omotopia dei percorsi mediante gli spazi di ricoprimento. Infine, si studiano gl’integrali di percorso per particelle identiche.
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Berg, H.P. Feynman path integrals on manifolds and geometric methods. Nuov Cim A 66, 441–449 (1981). https://doi.org/10.1007/BF02730365
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DOI: https://doi.org/10.1007/BF02730365