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Open AccessFeature PaperArticle

Descriptions of Relativistic Dynamics with World Line Condition

1
Max-Planck-Institut für Mathematik in den Naturwissenschaften. Inselstraße 22, 04103 Leipzig, Germany
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Dep.to de Matematica, Univ. Carlos III de Madrid. Av. da de la Universidad, 30, 28911 Leganes, Madrid, Spain
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ICMAT, Instituto de Ciencias Matematicas (CSIC-UAM-UC3M-UCM), Nicolás Cabrera, 13-15, Campus de Cantoblanco, UAM, 28049 Madrid, Spain
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INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo. Edificio 6, via Cintia, 80126 Napoli, Italy
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Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126 Napoli, Italy
*
Author to whom correspondence should be addressed.
Quantum Reports 2019, 1(2), 181-192; https://doi.org/10.3390/quantum1020016
Received: 14 September 2019 / Revised: 14 October 2019 / Accepted: 15 October 2019 / Published: 19 October 2019
In this paper, a generalized form of relativistic dynamics is presented. A realization of the Poincaré algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in R 4 . The construction of this realization is explicitly shown to clarify the role of the commutation relations of the Poincaré algebra versus their description in terms of Poisson brackets in the no-interaction theorem. Moreover, a geometrical analysis of the “eleventh generator” formalism introduced by Sudarshan and Mukunda is outlined, this formalism being at the basis of many proposals which evaded the no-interaction theorem. View Full-Text
Keywords: relativistic dynamics; no-interaction theorem; world line condition relativistic dynamics; no-interaction theorem; world line condition
MDPI and ACS Style

Ciaglia, F.M.; Di Cosmo, F.; Ibort, A.; Marmo, G. Descriptions of Relativistic Dynamics with World Line Condition. Quantum Reports 2019, 1, 181-192.

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