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Abstract:

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).

Registro:

Documento: Artículo
Título:Relativistic dynamics, Green function and pseudodifferential operators
Autor:Cirilo-Lombardo, D.J.
Filiación:National Institute of Plasma Physics (INFIP), Facultad de Ciencias Exactas y Naturales, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russian Federation
Año:2016
Volumen:57
Número:6
DOI: http://dx.doi.org/10.1063/1.4953368
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.
ISSN:00222488
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v57_n6_p_CiriloLombardo

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Citas:

---------- APA ----------
(2016) . Relativistic dynamics, Green function and pseudodifferential operators. Journal of Mathematical Physics, 57(6).
http://dx.doi.org/10.1063/1.4953368
---------- CHICAGO ----------
Cirilo-Lombardo, D.J. "Relativistic dynamics, Green function and pseudodifferential operators" . Journal of Mathematical Physics 57, no. 6 (2016).
http://dx.doi.org/10.1063/1.4953368
---------- MLA ----------
Cirilo-Lombardo, D.J. "Relativistic dynamics, Green function and pseudodifferential operators" . Journal of Mathematical Physics, vol. 57, no. 6, 2016.
http://dx.doi.org/10.1063/1.4953368
---------- VANCOUVER ----------
Cirilo-Lombardo, D.J. Relativistic dynamics, Green function and pseudodifferential operators. J. Math. Phys. 2016;57(6).
http://dx.doi.org/10.1063/1.4953368