Relativistic dynamics, Green function and pseudodifferential operators

The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of...

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Autor principal: Cirilo, Diego Julio
Publicado: 2016
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v57_n6_p_CiriloLombardo
http://hdl.handle.net/20.500.12110/paper_00222488_v57_n6_p_CiriloLombardo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00222488_v57_n6_p_CiriloLombardo
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spelling paper:paper_00222488_v57_n6_p_CiriloLombardo2023-06-08T14:48:19Z Relativistic dynamics, Green function and pseudodifferential operators Cirilo, Diego Julio The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: It is a non-local, Lorentz invariant and does not have the same problems as the "local"position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework. © 2016 Author(s). Fil:Cirilo-Lombardo, D.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v57_n6_p_CiriloLombardo http://hdl.handle.net/20.500.12110/paper_00222488_v57_n6_p_CiriloLombardo
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 central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: It is a non-local, Lorentz invariant and does not have the same problems as the "local"position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework. © 2016 Author(s).
author Cirilo, Diego Julio
spellingShingle Cirilo, Diego Julio
Relativistic dynamics, Green function and pseudodifferential operators
author_facet Cirilo, Diego Julio
author_sort Cirilo, Diego Julio
title Relativistic dynamics, Green function and pseudodifferential operators
title_short Relativistic dynamics, Green function and pseudodifferential operators
title_full Relativistic dynamics, Green function and pseudodifferential operators
title_fullStr Relativistic dynamics, Green function and pseudodifferential operators
title_full_unstemmed Relativistic dynamics, Green function and pseudodifferential operators
title_sort relativistic dynamics, green function and pseudodifferential operators
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v57_n6_p_CiriloLombardo
http://hdl.handle.net/20.500.12110/paper_00222488_v57_n6_p_CiriloLombardo
work_keys_str_mv AT cirilodiegojulio relativisticdynamicsgreenfunctionandpseudodifferentialoperators
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