{"title":"从路径积分角度看预量化问题","authors":"P A Horvathy","doi":"arxiv-2402.17629","DOIUrl":null,"url":null,"abstract":"The quantum mechanically admissible definitions of the factor\n$\\exp\\big[(i/\\hbar)S(\\gamma)\\big]$ in the Feynman integral are put in bijection\nwith the prequantisations of Kostant and Souriau. The different allowed\nexpressions of this factor -- the inequivalent prequantisations -- are\nclassified. The theory is illustrated by the Aharonov-Bohm experiment and by\nidentical particles.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Prequantisation from the path integral viewpoint\",\"authors\":\"P A Horvathy\",\"doi\":\"arxiv-2402.17629\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The quantum mechanically admissible definitions of the factor\\n$\\\\exp\\\\big[(i/\\\\hbar)S(\\\\gamma)\\\\big]$ in the Feynman integral are put in bijection\\nwith the prequantisations of Kostant and Souriau. The different allowed\\nexpressions of this factor -- the inequivalent prequantisations -- are\\nclassified. The theory is illustrated by the Aharonov-Bohm experiment and by\\nidentical particles.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2402.17629\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.17629","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The quantum mechanically admissible definitions of the factor
$\exp\big[(i/\hbar)S(\gamma)\big]$ in the Feynman integral are put in bijection
with the prequantisations of Kostant and Souriau. The different allowed
expressions of this factor -- the inequivalent prequantisations -- are
classified. The theory is illustrated by the Aharonov-Bohm experiment and by
identical particles.
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