Path integral for the relativistic particle in curved space

The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen;...

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Autor principal: Ferraro, Rafael
Publicado: 1992
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_05562821_v45_n4_p1198_Ferraro
http://hdl.handle.net/20.500.12110/paper_05562821_v45_n4_p1198_Ferraro
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_05562821_v45_n4_p1198_Ferraro2023-06-08T15:42:12Z Path integral for the relativistic particle in curved space Ferraro, Rafael The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.). © 1992 The American Physical Society. Fil:Ferraro, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1992 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_05562821_v45_n4_p1198_Ferraro http://hdl.handle.net/20.500.12110/paper_05562821_v45_n4_p1198_Ferraro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.). © 1992 The American Physical Society.
author Ferraro, Rafael
spellingShingle Ferraro, Rafael
Path integral for the relativistic particle in curved space
author_facet Ferraro, Rafael
author_sort Ferraro, Rafael
title Path integral for the relativistic particle in curved space
title_short Path integral for the relativistic particle in curved space
title_full Path integral for the relativistic particle in curved space
title_fullStr Path integral for the relativistic particle in curved space
title_full_unstemmed Path integral for the relativistic particle in curved space
title_sort path integral for the relativistic particle in curved space
publishDate 1992
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_05562821_v45_n4_p1198_Ferraro
http://hdl.handle.net/20.500.12110/paper_05562821_v45_n4_p1198_Ferraro
work_keys_str_mv AT ferrarorafael pathintegralfortherelativisticparticleincurvedspace
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